Let and . (i) Find the value of for which the scalar projection of on equals . (ii)…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let

\mathbf{u}=(3\mathbf{i}-\mathbf{j}+2\mathbf{k})+t(\mathbf{i}+2\mathbf{j}-\mathbf{k})

and

\mathbf{v}=2\mathbf{i}-\mathbf{j}+2\mathbf{k}

. (i) Find the value of

t

for which the scalar projection of

\mathbf{u}

\mathbf{v}

equals

6

. (ii) For this value of

t

, determine the vector component of

\mathbf{u}

along

\mathbf{v}