Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then
the x component is V*Cos(A)
and the y component is V*Sin(A)
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The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
It depends on the vector!
If A + B = 0, this means that vector A is equal in magnitude but opposite in direction to vector B. In other words, the two vectors are anti-parallel to each other. This relationship indicates that the components of the two vectors cancel each other out when added together, resulting in a net vector of zero.
At what angle should a vector be directed to so that its x component is equal to its y component
In 2 dimensions the angle made by the displacement vector with the positive x-axis is arctan(y/x).