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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
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B
π4
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C
π2
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D
π
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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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