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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.
What are the Methods used in adding and subtracting vectors?
In adding vectors, you can use the head-to-tail method where you place the tail of the second vector at the head of the first vector. Then, the sum is the vector that goes from the tail of the first vector to the head of the second vector. In subtracting vectors, you can add the negative of the vector you are subtracting by using the same method as vector addition.
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.
Which are the three vectors that act along the mutually perpendicular direction?
The three vectors that act along mutually perpendicular directions are the unit vectors in the x, y, and z directions, namely, i, j, and k. These vectors form the basis for three-dimensional space and are commonly used in physics and mathematics.
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?
If one component of vector A is zero along the direction of vector B, it means the two vectors are orthogonal or perpendicular to each other. Their directions would be such that they are at a right angle to each other.
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.
Under what circumstances can a vector have components that are equal in magnitude?
(Magnitude of the vector)2 = sum of the squares of the component magnituides Let's say the components are 'A' and 'B', and the magnitude of the vector is 'C'. Then C2 = A2 + B2 You have said that C = A, so C2 = C2 + B2 B2 = 0 B = 0 The other component is zero.
Every vector can be represented as the sum of its?
Every vector can be represented as the sum of its orthogonal components. For example, in a 2D space, any vector can be expressed as the sum of two orthogonal vectors along the x and y axes. In a 3D space, any vector can be represented as the sum of three orthogonal vectors along the x, y, and z axes.
How do the magnitudes and direction pair?
Magnitude and direction are related in vector quantities. The magnitude represents the size of the vector, while the direction indicates the orientation of the vector in space. In a 2D plane, direction can be specified by an angle relative to a reference axis, while in 3D space, direction can be defined by using angles or unit vectors along the coordinate axes.
When two vectors are acting at a point along different directions how do we determine magnitude and direction of the resultant?
To find the magnitude and direction of the resultant vector, you can use the parallelogram law of vector addition. Add the two vectors together to form a parallelogram, then the diagonal of the parallelogram represents the resultant vector. The magnitude can be calculated using trigonometry, and the direction can be determined using angles or components.
