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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.
