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What is resolution of vector?
Spliting up of vector into its rectangular components is called resolution of vector
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
What is the result of multiplying vector components by a scalar?
If the scalar is > 1 the resultant vector will be larger and in the same direction. = 1 the resultant vector will be the same as the original vector. between 0 and 1 the resultant vector will be smaller and in the same direction. = 0 the resultant vector will be null. If the scalar is less than 0, then the pattern will be the same as above except that the direction of the resultant will be reversed.
How do you calculate the projection of a vector onto another vector?
If A and B are two vectors, the projection (C) of A on B is the vector that has the same slope as B with the length:To calculate C use the following property of the dot product:Using the above equation:Multiply and divide by | B | at the same time:In the resulting fraction, the top term is the same as the dot product, hence:To find the length of | C | with an unknown θ, and unknown direction, multiply it with the unit vector B:giving the final formula:taken from: http://en.wikipedia.org/wiki/Vector_projection
Can a vector have a zero magnitude if all of its components are zero?
If all the components of a vector are zero, the magnitude of the vector will always be zero.
Do the vector components double if the vector doubles with the same direction?
Yes, if a vector doubles in magnitude with the same direction, then its components will also double in value. This is because the components of a vector are directly proportional to its magnitude in the same direction.
What is component in vector?
In vector terms, a component refers to the portion of the vector along a particular direction or axis. It is the projection of the vector onto that specific direction. For example, a vector in two dimensions can be broken down into its horizontal and vertical components.
How a vector can be express in term of its rectangular component?
A vector can be expressed in terms of its rectangular components by breaking it down into its horizontal and vertical components. These components represent the projection of the vector onto the x and y axes. The vector can then be expressed as the sum of these components using the appropriate unit vectors (i and j for x and y directions, respectively).
Can a single vector be replaced by two vectors in the x and y directions.?
Yes, a single vector can be represented by two vectors in the x and y directions using vector decomposition. This is known as resolving a vector into its components and can be done using trigonometry. The x-component corresponds to the projection of the vector onto the x-axis, and the y-component corresponds to the projection of the vector onto the y-axis.
What are the components of a vector?
The components of a vector are magnitude and direction.
The components of a vector or what?
The components of a vector are magnitude and direction.
The components of a vector will be the same no matter what coordinate system is used to express that vector?
Yes, that is correct. The components of a vector, which represent its magnitude and direction in a particular coordinate system, are independent of the choice of coordinate system used to express the vector. This property is a fundamental characteristic of vectors in mathematics and physics.
What is resolution of vector?
Spliting up of vector into its rectangular components is called resolution of vector
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
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 is the result of multiplying vector components by a scalar?
If the scalar is > 1 the resultant vector will be larger and in the same direction. = 1 the resultant vector will be the same as the original vector. between 0 and 1 the resultant vector will be smaller and in the same direction. = 0 the resultant vector will be null. If the scalar is less than 0, then the pattern will be the same as above except that the direction of the resultant will be reversed.
How do you calculate the projection of a vector onto another vector?
If A and B are two vectors, the projection (C) of A on B is the vector that has the same slope as B with the length:To calculate C use the following property of the dot product:Using the above equation:Multiply and divide by | B | at the same time:In the resulting fraction, the top term is the same as the dot product, hence:To find the length of | C | with an unknown θ, and unknown direction, multiply it with the unit vector B:giving the final formula:taken from: http://en.wikipedia.org/wiki/Vector_projection
