Mathematics

Mathematics

Problem

Let

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

and

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

, where

k

is a real parameter. a. (i) In terms of

k

, find

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

. b. (ii) Determine the value(s) of

k

for which

\mathbf{u}

is perpendicular to

\mathbf{v}

. c. (iii) For

k=2

, calculate the scalar projection of

\mathbf{v}

on

\mathbf{u}

. Give your answer correct to two decimal places.

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