JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}|=1,|\vec{b}|=4\) and \(\vec{a} \cdot \vec{b}=2\). If \(\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}\) and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\alpha\), then \(192 \sin ^2 \alpha\) is equal to
- A \(43\)
- B \(45\)
- C \(40\)
- D \(48\)
Answer & Solution
Correct Answer
(D) \(48\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=(2 \overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \cdot \overrightarrow{\mathrm{b}}-3|\mathrm{~b}|^2 \) \(|\mathrm{~b}||\mathrm{c}| \cos \alpha=-3|\mathrm{~b}|^2 \)…
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