Let and , where is a real parameter. Answer the following…

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

\vec{u}=(2t)\mathbf{i}+\mathbf{j}+t\mathbf{k}

and

\vec{v}=\mathbf{i}+t\mathbf{j}-\mathbf{k}

, where

t

is a real parameter. Answer the following questions. (i) Find all real values of

t

for which

\vec{u}

and

\vec{v}

are perpendicular. (ii) If the angle between

\vec{u}

and

\vec{v}

60^{\circ}

, determine the possible value(s) of

t

. (iii) For

t=2

, decide whether the angle between

\vec{u}

and

\vec{v}

is acute or obtuse and justify your conclusion.