Let the position vectors of points and with respect to the origin be and respectively.

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let the position vectors of points

A(2,-1,4)

and

B(-3,5,1)

with respect to the origin be

\mathbf{a}

and

\mathbf{b}

respectively. (i) Find the vectors

\mathbf{a}

and

\mathbf{b}

in component form. (ii) Calculate the exact value of the angle

\angle AOB

between

\mathbf{a}

and

\mathbf{b}

, where

O

is the origin. (iii) State whether the angle obtained in part (ii) is acute, right or obtuse, giving a reason based on your calculation.