Let and . It is known that the length of the projection of on equals…

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

Problem

Let

\vec a = 2\mathbf{i} + p\mathbf{j} + 3\mathbf{k}

and

\vec b = \mathbf{i} - \mathbf{j} + \mathbf{k}

. It is known that the length of the projection of

\vec a

\vec b

equals

\dfrac{4}{\sqrt{3}}

units. (i) Find the possible value(s) of the real parameter

p

. (ii) For each value of

p

obtained in part (i), determine the angle (to the nearest degree) between

\vec a

and

\vec b

. (iii) State, with reasons, whether each angle found in part (ii) is acute or obtuse.