Let hat{a} and hat{b} be two unit vectors. If | vedclass

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(C) Let $	heta$ be the angle between $\hat{a}$ and $\hat{b}$.Since $\bar{c}=\hat{a}+2 \hat{b}$ and $\bar{d}=5 \hat{a}-4 \hat{b}$ are perpendicular,th

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$\frac{\pi}{3}$

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(C) Let $	heta$ be the angle between $\hat{a}$ and $\hat{b}$.Since $\bar{c}=\hat{a}+2 \hat{b}$ and $\bar{d}=5 \hat{a}-4 \hat{b}$ are perpendicular,their dot product is zero.$\bar{c} \cdot \bar{d} = 0$$(\hat{a}+2 \hat{b}) \cdot (5 \hat{a}-4 \hat{b}) = 0$$5(\hat{a} \cdot \hat{a}) - 4(\hat{a} \cdot \hat{b}) + 10(\hat{b} \cdot \hat{a}) - 8(\hat{b} \cdot \hat{b}) = 0$Since $\hat{a}$ and $\hat{b}$ are unit vectors,$|\hat{a}|=1$ and $|\hat{b}|=1$,and $\hat{a} \cdot \hat{a} = 1$,$\hat{b} \cdot \hat{b} = 1$.$5(1) + 6(\hat{a} \cdot \hat{b}) - 8(1) = 0$$6(\hat{a} \cdot \hat{b}) - 3 = 0$$6 \cos 	heta = 3$$\cos 	heta = \frac{3}{6} = \frac{1}{2}$$	heta = \cos^{-1}\left(\frac{1}{2}ight) = \frac{\pi}{3}$

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

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