MHT CET · Maths · Vector Algebra
If \(\frac{\pi}{2} < \theta \leq\) and \(|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=13,|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25\), then the value of \(\bar{a} \cdot \bar{b}\) is
- A -12
- B 60
- C -60
- D -13
Answer & Solution
Correct Answer
(C) -60
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & |\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25 \\ & \therefore|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \sin \theta=(5)(13) \sin \theta=25 \\ & \therefore \sin \theta=\frac{5}{13} \Rightarrow \cos \theta=\frac{-12}{13} \\ & \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \cos \theta \\ & =(5)(13)\left(\frac{-12}{13}\right)=-60\end{aligned}\)
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