Question

# Let $$\overrightarrow{a}, \overrightarrow{b} ,\overrightarrow{c}$$ be non-coplanar vectors such that $$\overrightarrow{a}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)=\dfrac{\overrightarrow{b}}{2}$$, then the angle between $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$ is

A
3π4
B
π4
C
π2
D
π

Solution

## The correct option is C $$\dfrac{\pi}{2}$$$$\overrightarrow{a}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)=\dfrac{\overrightarrow{b}}{2}$$ (given)$$\Rightarrow \left(\overrightarrow{a}.\overrightarrow{c}\right)\overrightarrow{b}-\left(\overrightarrow{a}.\overrightarrow{b}\right)\overrightarrow{c}=\dfrac{\overrightarrow{b}}{2}$$$$\Rightarrow \overrightarrow{a}.\overrightarrow{b}=0 ,\left(\overrightarrow{a}.\overrightarrow{c}\right)\overrightarrow{b}=\dfrac{\overrightarrow{b}}{2}$$$$\Rightarrow \overrightarrow{a}.\overrightarrow{c}=\dfrac{1}{2}$$$$\therefore \overrightarrow{a}\bot \overrightarrow{b}$$Mathematics

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