Mathematics

Mathematics

Problem

Consider the vectors

\mathbf{a}=\langle k,2,-1\rangle

and

\mathbf{b}=\langle 3,-k,4\rangle

, where

k

is a real number. a. (i) Determine the value of

k

for which

\mathbf{a}

is perpendicular to

\mathbf{b}

. b. (ii) For the value of

k

obtained in part (i), compute

(\mathbf{a}+2\mathbf{b})\!\cdot\!(\mathbf{a}-\mathbf{b})

. c. (iii) Using your answer from part (ii), find

|\mathbf{a}+2\mathbf{b}|^{2}

.

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