JEE Mains · Maths · STD 12 - 10. vector algebra
If \(|\vec{a}|=2,|\vec{b}|=5\) and \(|\vec{a} \times \vec{b}|=8\), then \(|\vec{a} \cdot \vec{b}|\) is equal to :
- A \(5\)
- B \(4\)
- C \(6\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(|\vec{a}|=2,|\vec{b}|=5\) \(|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta=\pm 8\) \(\sin \theta=\pm \frac{4}{5}\) \(\therefore \vec{a} \cdot \vec{b}=|\vec{a}| \vec{b} \mid \cos \theta\) \(=10 \cdot\left(\pm \frac{3}{5}\right)=\pm 6\) \(|\vec{a} \cdot \vec{b}|=6\)
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