Let hat{alpha}, hat{beta}, hat{gamma} be thre | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $\hat{\alpha}, \hat{\beta}, \hat{\gamma}$ are unit vectors,so $|\hat{\alpha}| = |\hat{\beta}| = |\hat{\gamma}| = 1$.Using the vector tr

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(D) Given that $\hat{\alpha}, \hat{\beta}, \hat{\gamma}$ are unit vectors,so $|\hat{\alpha}| = |\hat{\beta}| = |\hat{\gamma}| = 1$.Using the vector triple product formula: $\hat{\alpha} 	imes (\hat{\beta} 	imes \hat{\gamma}) = (\hat{\alpha} \cdot \hat{\gamma}) \hat{\beta} - (\hat{\alpha} \cdot \hat{\beta}) \hat{\gamma}$.Given the equation: $(\hat{\alpha} \cdot \hat{\gamma}) \hat{\beta} - (\hat{\alpha} \cdot \hat{\beta}) \hat{\gamma} = \frac{1}{2} \hat{\beta} + \frac{1}{2} \hat{\gamma}$.Since $\hat{\beta}$ and $\hat{\gamma}$ are not parallel,we can compare the coefficients of $\hat{\beta}$ and $\hat{\gamma}$ on both sides.Comparing the coefficients of $\hat{\gamma}$,we get: $-(\hat{\alpha} \cdot \hat{\beta}) = \frac{1}{2}$.Thus,$\hat{\alpha} \cdot \hat{\beta} = -\frac{1}{2}$.Since $\hat{\alpha} \cdot \hat{\beta} = |\hat{\alpha}| |\hat{\beta}| \cos 	heta$,where $	heta$ is the angle between $\hat{\alpha}$ and $\hat{\beta}$,we have $1 	imes 1 	imes \cos 	heta = -\frac{1}{2}$.Therefore,$\cos 	heta = -\frac{1}{2}$,which implies $	heta = \frac{2 \pi}{3}$.

Let $\hat{\alpha}, \hat{\beta}, \hat{\gamma}$ be three unit vectors such that $\hat{\alpha} \times (\hat{\beta} \times \hat{\gamma}) = \frac{1}{2}(\hat{\beta} + \hat{\gamma})$. If $\hat{\beta}$ is not parallel to $\hat{\gamma}$,then the angle between $\hat{\alpha}$ and $\hat{\beta}$ is

Similar Questions

Let $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2 \hat{i}-3 \hat{j}+2 \hat{k}$. Then the number of vectors $\vec{b}$ such that $\vec{b} \times \vec{c}=\vec{a}$ and $|\vec{b}| \in\{1, 2, \ldots, 10\}$ is

If $\bar{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \bar{b}=-\hat{i}+2 \hat{j}-4 \hat{k}$ and $\bar{c}=\hat{i}+\hat{j}-2 \hat{k}$,then $(\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=$

If $\bar{a}=2\hat{i}+3\hat{j}-\hat{k}$,$\bar{b}=-\hat{i}+2\hat{j}-4\hat{k}$ and $\bar{c}=\hat{i}+\hat{j}+\hat{k}$,then $(\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=$

Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$,$\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}$ and a vector $\vec{c}$ be such that $2(\vec{a} \times \vec{c}) + 3(\vec{b} \times \vec{c}) = \vec{0}$. If $\vec{a} \cdot \vec{c} = 15$,then $\vec{c} \cdot (\hat{i} + \hat{j} - 3\hat{k})$ is equal to:

Let $ABCD$ be a quadrilateral with $\overline{AB}=\bar{a}$,$\overline{AD}=\bar{b}$ and $\overline{AC}=3\bar{a}+2\bar{b}$. If its area is $\alpha$ times the area of the parallelogram with $AB$ and $AD$ as adjacent sides,then the value of $\alpha$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module