Let and , where is a real…

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

Problem

Let

\mathbf{u}=(k,2,-1)

and

\mathbf{v}=(3,k-1,4)

, where

k

is a real parameter. (i) In terms of

k

, find

\mathbf{u}\cdot\mathbf{v}

. (ii) Determine the value(s) of

k

for which

\mathbf{u}

is perpendicular to

\mathbf{v}

. (iii) For

k=2

, calculate the scalar projection of

\mathbf{v}

\mathbf{u}

. Give your answer correct to two decimal places.