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What are the projections of a vector along the axes of a coordinate system?
Wiki User
∙ 9y ago
A tangent of the vector is the projection of a vector along the axes of a coordinate system.
Wiki User
∙ 9y ago
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Can a vector directed along x-axis have y-axis component?
At what angle should a vector be directed to so that its x component is equal to its y component
What coordinate is used to locate points on grids?
Not a coordinate but a pair (or larger set) of coordinates.These are ordered sets of numbers that give the distance of the point, from the origin, along each of the axes in multidimensional space.
What is the x-coordinate?
You kinda need to be more specific about the context. But that never stopped me from trying! If you are looking at a 2 dimensional graph then the X-axis drawn from horizontally (left-right). The X-coordinate is the position along the X-axis. Happy plotting!
What is the Definition of Cartesian coordinate system?
A system for identifying points on a plane or in space by their coordinates is called a Cartesian coordinate system.In a plane (2-dimensional), the Cartesian coordinate system is determined by the two perpendicular directed lines Ox as x-axis, and Oy as y-axis (where the point of intersection O is the origin) and the given unit length.For any point P in the plane, let M and Nbe points on the x-axis and y-axis such that PM is parallel to y-axis and PN is parallel to x-axis. If OM = x and ON = y, then (x, y) are the coordinates of the point P in this Cartesian coordinate system.Normally, Ox and Oy are chosen so that an an anticlockwise rotation of one right angle takes the positive x-direction to the positive y-direction.In 3-dimensional space, the Cartesian coordinate system is determined by the three mutually perpendicular directed lines Ox as x-axis, and Oy as y-axis,and OZ as z-axis (where the point of intersection O is the origin).For any point P in a space, let L be the point where the plane through P, parallel to the plane containing the y-axis and z-axis, meets the x-axis. Alternatively, L is the point on the x-axis such that PL is perpendicular to the x-axis. Let M and N be points on the y-axis and z-axis. The points L, M, and N are in fact three of vertixes of the cuboid with three of its edges along the coordinate axes and with O and P as opposite vertixes. If OL = x and OM = y, and ON = z, then (x, y, z) are the coordinates of the point P in this Cartesian coordinate system.
How do you graph a vector in component form?
Select two axes in a 2-d plane along which you want the vector components (3 axes in 3-d and so on). The axes must meet at a point, but need not be perpendicular.In 2-d, draw a parallelogram so that its diagonal is the given vector and the adjacent sides are parallel to the axes. These adjacent sides will represent the components of the vector.If the axes are at right angles and the vector Vmakes an angle t with the positive horizontal axis, thenhorizontal component = V*costandvertical component = V*sint
When you resolve a vector and what do you get?
You get other vectors, usually perpendicular to each other, that - when added together - result in the original vector. These component vectors are usually along the axes of some selected coordinate system.
How do you name the direction of a vector?
The direction of a vector is defined in terms of its components along a set of orthogonal vectors (the coordinate axes).
Can you add three unit vectors to get a unit vector does your answer change if two unit vectors are along the coordinate axes?
Yes., and their being along the coordinate axes does not change the answer.Consider the vectors: i, -i and j where i is the unit vector along the x axis and j along the y axis. The resultant of the three is j.
Can a vector have 0 component along a line and still have non zero magnitude?
Huh?I have been kicking around your question in my mind for five minutes trying to figure out an answer or a way to edit your question into an unambiguous form, but I'm stumped. I don't know what you mean by "zero component along a line."If you look at the representation of a vector on paper using a Cartesian coordinate system -- in other words, one using x and y axes -- the orthogonal components of the vector are the projections of the vector on the x and y axes. If the vector is parallel to one of the axes, its projection on the other axis will be zero. But the vector will still have a non-zero magnitude. Its entire magnitude will project on only one axis.But a vector must have magnitude AND direction. And if it has zero magnitude, its direction cannot be determined.Still trying to make heads or tails out of your question.......If you draw a random vector on a Cartesian grid, it will have an x component and a y component, which are both projections of the original vector upon the axes. However, it could also be represented by projecting it onto a new set of orthogonal axes -- call them x' and y' -- where the x' axis is oriented to be parallel to the original vector and the y' vector is perpendicular to it. In that case, the x' component will have a magnitude equal to the magnitude of the original vector -- in other words, a non-zero value along a line parallel to the x' axis -- and a zero magnitude in the y' direction.
What is an abscissa?
An abscissa is the coordinate representing the position of a point along a line perpendicular to the y-axis in a plane Cartesian coordinate system.
Is a torque vector quantity?
Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.Yes. The "direction" of the vector is along the axis of rotation.
What is meant by a component of a vector?
A component of a vector can be thought of as an "effectiveness" of that vector in a given direction. It's actually a "piece" or "part" of the vector. A vector is a geometric object with the two characteristics of direction and magnitude. It is when we plot these in a coordinate system that we see the components appear. If we draw a graph with the standard x and y coordinates handed down to us from Descartes, we can more easily see the components. On the graph, draw a vector from the origin (0,0) to the point (5,5). We set the origin as the point of initiation of the vector, and the "little arrow" on the "head" or terminus of the vector is at (5,5). But that vector represents the sum of two other vectors. One is the vector from the origin that runs along the x-axis to (5,0) and the other is the vector that runs from the origin along the y-axis to (0,5). As stated, the sum of these other two vectors makes the original vector we drew. And each of these vectors, the x and y vectors we drew, is a component of the vector we are inspecting. The components of vectors can be expanded into a multitude of dimensions, and will be dependent on the system we use to plot them. Wikipedia has some additional information, and a link is provided.
What is the maximun no of components into which a vector can be split?
There is no maximum. A vector can be defined for a hyperspace with any number of dimensions. Such a hyperspace can be described using an orthogonal system of axes and the vector can be split into its components along each one of these axes.
Can the components of a vector be different in different coordinate systems?
Apparently so. I answered False and was wrong. I don't really understand how though seeing as magnitude and direction cannot be different, and they are determined by the components, but oh well. The answer is True. * * * * * Translation of the axis will not make a difference to the components but rotation will. Here is a simplified explanation (I hope), with more mathematical details for those who want it. The components of a vector are the projections of the vector along the coordinate axes. If you have a vector, its component along the x-axis is what its "shadow" on the x-axis would be if you shone the light from above - from a direction perpendicular to the x-axis. And its component along the y-axis would be the shadow if you shone a light from a direction perpendicular to the y-axis. Leave the vector as it is and rotate the coordinate axes about the origin and see what happens. The components will change. More advanced: Suppose the original vector, V, had a length of r units and made an angle of A with the x-axis at the origin. then Vx = r*cos(A) and Vy = r*sin(A) Now rotate the axes (anticlockwise) by an angle B. V now makes an angle (A-B) with the new x-axis. then Vx' = r*cos(A-B) and Vy' = r*sin(A-B) These will not be the same unless B = 2*pi*k where k is an integer. That is, only if the axes were rotated through a whole number of circles - back to where it was!
When should you express a vector along the x-axis as a negative vector?
You express a vector along the X-axis as a negative vector when the arrow representing the vector would point toward negative x.
A vector a is along the positive z axis and it's vector product with another vector b is zero then vector b could be?
Vector b would be along the z axis, it could have any magnitude.
If i have a points a and b in 3d space and i want to move b n units closer to a how do i determine how much to change b's x y and z values?
How to move a specific distance along a line determined by 2 points in 3d space! Specific distance = m Distance between the 2 points = D Distance to move along line from Point #2 toward Point #1 = Displacement = m Determine the coordinates of the point M (c, d, e), which is m units closer to Point#2 Given 2 points Point #1 (a, b, c) Point #2 (g. h, i) 1. Find the distance between the 2 points using Pythagorean Theorem Think of moving from Point #1 to Point #2 by moving along the x-axis, then the y-axis, then the z-axis. (g-a) = distance moved along the x-axis (h-b) = distance moved along the y-axis (i-c) = distance moved along the x-axisS D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5 2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D. Coordinates of unit vector = [(g-a) ÷ D], [(h-b) ÷ D], [(i-c) ÷ D] x coordinate of unit vector = (g-a) ÷ D y coordinate of unit vector = (h-b) ÷ D z coordinate of unit vector = (i-c) ÷ D Unit vector = [((g-a) ÷ D)^2 + ((h-e) ÷ D) ^2) + ((i-c) ÷ D) ^2]^0.5) = 1 If the value of the unit vector does not =1, go back and check your work. 3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m. These coordinates will be added to coordinates of Point #1 to determine the coordinates of Point #3. x coordinate of m vector = m * (g-a) ÷ D y coordinate of m vector = m * (h-b) ÷ D z coordinate of m vector = m * (i-c) ÷ D 4. To determine the coordinates of Point #3(d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1. d = x coordinate of Point #3 = a + (m * (g-a) ÷ D) e = y coordinate of Point #3 = b + (m * (h-b) ÷ D) f = z coordinate of Point #3 = c + (m * (i-c) ÷ D) 5. To determine the distance from Point #1 (a, b, c) to Point #3 (d, e, f), use Pythagorean Theorem D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5 The answer should be m. I wanted to move 2 cm from Point #1 toward Point #2, and I did. Now let's see if this method works!! Point #1 = (2,3,1), Point #2 = (6,9,3) I want to move 2 cm from Point #1 toward Point #2, that means m = 2 cm. 1. Find the distance between the 2 points using Pythagorean Theorem D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5 D = [(6-2)^2 + (9-3)^2 + (3-1)^2]^0.5 D = [(4)^2 + (6)^2 + (2)^2]^0.5 D = [16 + 36 + (4)]^0.5 D = 56^0.5 D = 7.4833 So the line between these Point #1 and Point #2 is 7.483 units long 2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D. Distance moved along x-axis = 4 Distance moved along y-axis = 6 Distance moved along z-axis = 2 x-coordinate of unit vector = 4 ÷ 7.4833 = 0.5345 y-coordinate of unit vector = 6 ÷ 7.483 = 0.8018 z-coordinate of unit vector = 2 ÷ 7.483 = 0.2673 Length of unit vector = [(0.5345)^2 + (0.8018)^2+ (0.2673)^2]^0.5 = 1 The length of the unit vector should = 1 3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m. x coordinate of m vector = m * (g-a) ÷ D = 2 * 0.5345 = 1.069 y coordinate of m vector = m * (h-b) ÷ D = 2 * 0.8018 = 1.6036 z coordinate of m vector = m * (i-c) ÷ D = 2 * 0.2673 = 0.5346 m vector = [1.069^2 + (1.6036)^2 + (1.5346)^2]^0.5 = 2 4. To determine the coordinates of the Point #3 (d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1 (a, b, c). Point #1 = (2, 3, 1) x coordinate of Point #3 = 2 + 1.069 = 3.069 y coordinate of Point #3 = 3 +1.6036 = 4.6036 z coordinate of Point #3 = 1+ 0.5346 = 1.5346 Point #3 = (3.069, 4.6036, 1.5346) 5. To determine the distance from Point#1 to Point #3, use Pythagorean Theorem D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5 D = [(3.069-2)^2 + (4.6036-3)^2 + (1.5346-1)^2]^0.5 D = [(1.069)^2 + (1.6036)^2 + (0.5346)^2]^0.5 = 2 D = 2 cm I wanted to move 2 cm from Point #1 toward Point #2, and I did.
