Question

Let \(\vec{a}\) = 2\(\widehat{i}\)+3\(\widehat{j}\)+4\(\widehat{k}\), \(\vec{b}\) = \(\widehat{i}\)-2\(\widehat{j}\)-2\(\widehat{k}\), \(\vec{c}\) = -\(\widehat{i}\)+4\(\widehat{j}\)+3\(\widehat{k}\) and \(\vec{d}\) is a vector perpendicular to \(\vec{b}\) and \(\vec{c}\),  \(\vec{a}\).\(\vec{d}\) = 18, then find |\(\vec{a}\)x\(\vec{d}\)|²

• A. 720
• B. 700
• C. 360
• D. 300

Answer 1

The Correct Option is A

\(\vec{d}=\lambda (\vec{b}\times \vec{c})=\lambda (2\widehat{i}-\widehat{j}+2\widehat{k})\)
\(\vec{a}.\vec{d}=18\)
\(\Rightarrow \lambda =2\)
Therefore, \(|\vec{a}\times \vec{d}|^{2}=\vec{a}^{2}\vec{d}^{2}-(\vec{a}.\vec{d})^{2}\)
\(\Rightarrow |\vec{a}\times \vec{d}|^{2}=29\times 36-324=1044-324=720\)