If $\mathbf{a}$ is a vector of magnitude $7, \mathbf{b}$ is a vector of magnitude 8 , then the maximum value…
If $\mathbf{a}$ is a vector of magnitude $7, \mathbf{b}$ is a vector of magnitude 8 , then the maximum value of $\mathbf|{a} \cdot \mathbf{b}|$ is
- 5 and $(\mathbf{a} \cdot \mathbf{b})=\frac{\pi}{6}$
- 28 and $(\mathbf{a} \cdot \mathbf{b})=\frac{\pi}{3}$
- 56 and $(\mathbf{a} \cdot \mathbf{b})=\frac{\pi}{2}$
- 56 and $(\mathbf{a} \cdot \mathbf{b})=\pi$
Solution
Given, $|\mathbf{a}|=7$ and $|\mathbf{b}|=8$
$\mathbf{a} \cdot \mathbf{b}=|\mathbf{a}||\mathbf{b}| \cos \theta$
$\begin{aligned} & |\mathbf{a} \cdot \mathbf{b}|=|\mathbf{a}||\mathbf{b}| \cos \theta \\ & |\mathbf{a} \cdot \mathbf{b}|=7 \times 8|\cos \theta| \\ & |\mathbf{a} \cdot \mathbf{b}|=56|\cos \theta|\end{aligned}$
$|\mathbf{a} \cdot \mathbf{b}|$ is maximum when $\theta=\pi$
and maximum value is 56.
Asked in: AP EAMCET 2021 (24 Aug Shift 2)
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