JEE Advance - Mathematics (2010 - Paper 1 Offline - No. 21)
If $$\overrightarrow a $$ and $$\overrightarrow b $$ are vectors in space given by $$\overrightarrow a = {{\widehat i - 2\widehat j} \over {\sqrt 5 }}$$ and $$\overrightarrow b = {{2\widehat i + \widehat j + 3\widehat k} \over {\sqrt {14} }},$$ then find the value of $$\,\left( {2\overrightarrow a + \overrightarrow b } \right).\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a - 2\overrightarrow b } \right)} \right].$$
Answer
5
Explanation
$$ \begin{aligned} & (2 \vec{a}+\vec{b})[(\vec{a} \times \vec{b}) \times(\vec{a}-2 \vec{b})] \\\\ & =4(\vec{a} \cdot \vec{a})+\vec{b} \cdot \vec{b}+4 \vec{a} \cdot \vec{b} \text { where } \\\\ & \vec{a} \cdot \vec{b}=\frac{2-2}{\sqrt{70}}=0 \quad|\vec{a}|=1 \text { and }|\vec{b}|=1 \\\\ & =5 \end{aligned} $$
Comments (0)
