The vectors and form two sides of a triangle

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

Problem

The vectors

\mathbf{p}=2\hat{i}-\hat{j}+\hat{k}

and

\mathbf{q}=3\hat{i}+4\hat{j}+\lambda\hat{k}

form two sides of a triangle. If the area of the triangle is

5\sqrt{2}

square units, determine the value(s) of

\lambda