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Can you add three unit vectors to get a unit vector does your answer change if two unit vectors are along the coordinate axes?
Wiki User
∙ 12y ago
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.
Wiki User
∙ 12y ago
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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).
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.
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
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 purpose of vector resolution in adding vectors?
Vector addition does not follow the familiar rules of addition as applied to addition of numbers. However, if vectors are resolved into their components, the rules of addition do apply for these components. There is a further advantage when vectors are resolved along orthogonal (mutually perpendicular) directions. A vector has no effect in a direction perpendicular to its own direction.
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).
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.
What are the projections of a vector along the axes of a coordinate system?
A tangent of the vector is the projection of a vector along the axes of a coordinate system.
If the component of vector A along the direction of vector B is zero. What can you conclude about these two vectors?
Their directions are perpendicular.
If one component of a vector A is zero along the direction of another vector B then in what direction the two vectors will be?
opposite direction.
Which are the three vectors that act along the mutually perpendicular direction?
cross product of tow vector result in a vector which is perpendicular the multiplying vector then these three vector are perpedicular
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 purpose of vector resolution in adding vectors?
Vector addition does not follow the familiar rules of addition as applied to addition of numbers. However, if vectors are resolved into their components, the rules of addition do apply for these components. There is a further advantage when vectors are resolved along orthogonal (mutually perpendicular) directions. A vector has no effect in a direction perpendicular to its own direction.
If vector A is perpendicular to vector B and C then Vector A is parallel to?
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.
When two vectors are acting at a point along different directions how do we determine magnitude and direction of the resultant?
The usual way to do this is to express each vector as the sum of two or three perpendicular vectors (two in a plane, three in 3D space). Then you can add the components of the two vectors, to get the new vector.For the case of two dimensions, on most scientific calculators there is a neat feature called rectangular-to-polar and polar-to-rectangular conversion, which can quickly convert a vector from polar (i.e., magnitude and angle) to rectangular (i.e., x-coordinate and y-coordinate), or vice versa.
What are Two basic ways of adding vectors?
The first way is graphical: draw the vectors head to tail and draw a new vector with a tail having the same tail as the first vector and having the same head as the second vector. This new vector is the sum of the two.The other way is arithmetic: Gets the components of the vectors along a set of Cartesian axis. The ith component of the sum is the ith component of the first vector plus the ith component of the second vector.
Can three vectors not in one plane give zero resultant?
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
