MHT CET · Maths · Vector Algebra
If \(|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4\) and \(\overline{\mathrm{a}}\) is perpendicular to \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) such that angle between \(\bar{b}\) and \(\bar{c}\) is \(\frac{5 \pi}{6}\), then \([\bar{a} \bar{b} \bar{c}]=\)
- A 25
- B 10
- C 30
- D 20
Answer & Solution
Correct Answer
(C) 30
Step-by-step Solution
Detailed explanation
\([\vec{a} \vec{b} \vec{c}]=|\vec{a}||\vec{b}||\vec{c}| \cdot(\cos\) of angle between \(\vec{a}\) and \(\vec{b} \times \vec{c})\).(sin of angle between \(\vec{b}\) and \(\vec{c}\) )
\(\begin{aligned} & =5 \times 3 \times 4 \times \cos 0 \times \sin \left(\frac{5 \pi}{6}\right) \\ & =60 \times 1 \times \frac{1}{2}=30\end{aligned}\)
\(\begin{aligned} & =5 \times 3 \times 4 \times \cos 0 \times \sin \left(\frac{5 \pi}{6}\right) \\ & =60 \times 1 \times \frac{1}{2}=30\end{aligned}\)
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