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CBSE Class 12 Math 2023 All Sets Solved Paper

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Question : 6 of 20
Marks: +1, -0
If ∣a⃗×b⃗∣=3\left|\vec{a}\times\vec{b}\right| = \sqrt{3} and a⃗⋅b⃗=−3,\vec{a}\cdot\vec{b} = -3, then angle between a⃗\vec{a} and b⃗\vec{b} is
Solution:  
Given ∣a⃗×b⃗∣=3\left|\vec{a}\times\vec{b}\right| = \sqrt{3} and a⃗⋅b⃗=−3\vec{a}\cdot\vec{b} = -3
⇒∣a⃗∣∣b⃗∣∣sin⁡θ∣=3 and ∣a⃗∣∣b⃗∣cos⁡θ=−3\Rightarrow \left|\vec{a}\right|\left|\vec{b}\right|\left|\sin\theta\right| = \sqrt{3} \text{ and } \left|\vec{a}\right|\left|\vec{b}\right|\cos\theta = -3
Dividing both equations, we get
tan⁡θ=−13\tan\theta = -\frac{1}{\sqrt{3}}
⇒θ=5π6\Rightarrow \theta = \frac{5\pi}{6}
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