Points and are the ends of a directed line segment representing a force

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Points

A(2,-1,3)

and

B(5,4,-2)

are the ends of a directed line segment representing a force. (a) Obtain the vector

\overrightarrow{AB}

in component form. (b) Calculate the magnitude of

\overrightarrow{AB}

. (c) Find the unit vector along

\overrightarrow{AB}

. (d) Determine the unit vector in the direction opposite to

\overrightarrow{AB}

. (e) Using your result in part (b), write the direction cosines of

\overrightarrow{AB}

correct to two decimal places.