Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2 \hat{b}$ and $\vec{d}=5 \hat{a}-4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ is

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Aicharya · Accepted Answer

$\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{d}}=\overrightarrow{0} \quad \Rightarrow 5|\overrightarrow{\mathrm{a}}|^2+6 \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}-8|\overrightarrow{\mathrm{b}}|^2=0$ $\Rightarrow 6 \vec{a} \cdot \vec{b}=3 \quad \Rightarrow \vec{a} \cdot \vec{b}=\frac{1}{2} \quad \Rightarrow(\vec{a} \cdot \vec{b})=\frac{\pi}{3}$

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2 \hat{b}$ and $\vec{d}=5…

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