If $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=13,|\overline{\mathrm{a}} \times…

If $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=13,|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25$, then the value of $\bar{a} \cdot \bar{b}$ is
  1. -12
  2. 60
  3. -30
  4. -13

Solution

$\begin{aligned} & |\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25 \\ & \therefore|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \sin \theta=(5)(13) \sin \theta=25 \\ & \therefore \sin \theta=\frac{5}{13} \Rightarrow \cos \theta=\frac{+12}{13} \\ & \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \cos \theta \\ & =(5)(13)\left(\frac{+12}{13}\right)=+60\end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

Practice more Vectors questions on Aicharya