hat{a}, hat{b},and hat{c} are three unit vect | vedclass

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(A) Given the vector triple product identity: $\hat{a} 	imes (\hat{b} 	imes \hat{c}) = (\hat{a} \cdot \hat{c}) \hat{b} - (\hat{a} \cdot \hat{b}) \ha

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$\frac{5 \pi}{6}$

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(A) Given the vector triple product identity: $\hat{a} 	imes (\hat{b} 	imes \hat{c}) = (\hat{a} \cdot \hat{c}) \hat{b} - (\hat{a} \cdot \hat{b}) \hat{c}$.Comparing this with the given equation: $(\hat{a} \cdot \hat{c}) \hat{b} - (\hat{a} \cdot \hat{b}) \hat{c} = \frac{\sqrt{3}}{2} \hat{b} + \frac{\sqrt{3}}{2} \hat{c}$.Since $\hat{b}$ and $\hat{c}$ are not parallel,we can equate the coefficients of $\hat{b}$ and $\hat{c}$:$\hat{a} \cdot \hat{c} = \frac{\sqrt{3}}{2}$ and $-(\hat{a} \cdot \hat{b}) = \frac{\sqrt{3}}{2} \Rightarrow \hat{a} \cdot \hat{b} = -\frac{\sqrt{3}}{2}$.Let $	heta$ be the angle between $\hat{a}$ and $\hat{b}$. Since $\hat{a}$ and $\hat{b}$ are unit vectors,$\hat{a} \cdot \hat{b} = |\hat{a}| |\hat{b}| \cos 	heta = \cos 	heta$.Therefore,$\cos 	heta = -\frac{\sqrt{3}}{2}$.Since $\cos 	heta = -\frac{\sqrt{3}}{2}$,we have $	heta = \pi - \frac{\pi}{6} = \frac{5 \pi}{6}$.

$\hat{a}, \hat{b}$,and $\hat{c}$ are three unit vectors such that $\hat{a} \times(\hat{b} \times \hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})$. If $\hat{b}$ is not parallel to $\hat{c}$,then the angle between $\hat{a}$ and $\hat{b}$ is

Similar Questions

Let $a, b, c$ be three vectors. Determine the correctness of the following statements:
$(i)$ $(a \times b) \times c = (a \cdot c) b - (b \cdot c) a$
(ii) $a \times (b \times c) = (a \cdot c) b - (a \cdot b) c$

If $\bar{x} \cdot \bar{y} = 0$,then $\bar{x} \times (\bar{x} \times \bar{y}) = \dots$ where $|\bar{x}| = 1$.

If $a, b, c$ are non-coplanar unit vectors such that $a \times (b \times c) = \frac{b + c}{\sqrt{2}}$,then the angle between $a$ and $b$ is

Statement $(A)$ : If $\vec{a}$ is perpendicular to $\vec{b}$ and $\vec{c}$,then $\vec{a} \times (\vec{b} \times \vec{c}) = 0$.
Reason $(R)$ : If $\vec{b}$ is perpendicular to $\vec{c}$,then $\vec{b} \times \vec{c} = 0$.

Let $\vec{a}, \vec{b},$ and $\vec{c}$ be three unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c}) = \frac{\sqrt{3}}{2}(\vec{b} + \vec{c})$. If $\vec{b}$ is not parallel to $\vec{c}$,then the angle between $\vec{a}$ and $\vec{b}$ is:

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