Often a vector is specified by a magnitude and a direction; for example, a rope

Question

Often a vector is specified by a magnitude and a direction; for example, a rope with tension T_vec exerts a force of magnitude T in a direction 35 degrees north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Find the components of the vector with length a and angle alpha with respect to the x axis as shown, named A_vec. Don't forget that when multiplying two factors, you must include a multiplication symbol; also, the cos and sin functions must have parentheses around their arguments. For example, a vector might take the form p*sin(Q),m*cos(N) Write the components in the form x, y.

Explanation / Answer

A = a ( cos alpha , sin alpha) = (a*cos alpha ,a*sin alpha)

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