Question

The area of the parallelogram whose adjacent sides are $\hat{i}+ \hat {k} $ and $2\hat {i}+\hat {j}+\hat {k}$ is

• A. $\sqrt {2}$
• B. $\sqrt {3}$
• C. $3$
• D. $4$

Answer 1

The Correct Option is B

The correct answer is B:\(\sqrt{3}\)
Let adjacent sides of a parallelogram are
\(a =\hat{ i }+\hat{ k }\) and \(b =2 \hat{ i }+\hat{ j }+\hat{ k }\)
\(\therefore\) Area of parallelogram \(=\| a \times b \|\)
\(\begin{Vmatrix}\hat{i}&\hat{j}&\hat{k}\\ 1&0&1\\ 2&1&0\end{Vmatrix}\)
\(=|\hat{ i }(0-1)-\hat{ j }(1-2)+\hat{ k }(1-0)|\)
\(\therefore |\vec{a}\times\vec{b}|=|-\hat{ i }+\hat{ j }+\hat{ k }|\)
\(=\sqrt{(-1)^{2}+(1)^{2}+(1)^{2}}= \sqrt{3}\space sq.unit\)