Let bar{a}, bar{b} and bar{c} be three unit v | vedclass

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

Question

(D) Given the vector triple product formula: $\bar{a} 	imes (\bar{b} 	imes \bar{c}) = (\bar{a} \cdot \bar{c}) \bar{b} - (\bar{a} \cdot \bar{b}) \bar

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Given the vector triple product formula: $\bar{a} 	imes (\bar{b} 	imes \bar{c}) = (\bar{a} \cdot \bar{c}) \bar{b} - (\bar{a} \cdot \bar{b}) \bar{c}$.Comparing this with the given equation $\bar{a} 	imes (\bar{b} 	imes \bar{c}) = \frac{\sqrt{3}}{2} \bar{b} + \frac{\sqrt{3}}{2} \bar{c}$,we have:$(\bar{a} \cdot \bar{c}) \bar{b} - (\bar{a} \cdot \bar{b}) \bar{c} = \frac{\sqrt{3}}{2} \bar{b} + \frac{\sqrt{3}}{2} \bar{c}$.Since $\bar{b}$ and $\bar{c}$ are not parallel,we can equate the coefficients of $\bar{b}$ and $\bar{c}$:$\bar{a} \cdot \bar{c} = \frac{\sqrt{3}}{2}$ and $-(\bar{a} \cdot \bar{b}) = \frac{\sqrt{3}}{2}$,which implies $\bar{a} \cdot \bar{b} = -\frac{\sqrt{3}}{2}$.Let $	heta$ be the angle between $\bar{a}$ and $\bar{b}$. Since $\bar{a}$ and $\bar{b}$ are unit vectors,$|\bar{a}| = 1$ and $|\bar{b}| = 1$.$\bar{a} \cdot \bar{b} = |\bar{a}| |\bar{b}| \cos 	heta = 1 	imes 1 	imes \cos 	heta = \cos 	heta$.Thus,$\cos 	heta = -\frac{\sqrt{3}}{2}$.Since $\cos 	heta = -\frac{\sqrt{3}}{2}$,the angle $	heta = \frac{5 \pi}{6}$.

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

Similar Questions

If the area of a parallelogram,whose diagonals are $\vec{d_1} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{d_2} = 2\hat{i} + 3\hat{j} + \alpha\hat{k}$,is $\frac{\sqrt{93}}{2}$ sq. unit,then $\alpha = $

$A$ unit vector perpendicular to both the vectors $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$ is

The unit vector perpendicular to $3i + 2j - k$ and $12i + 5j - 5k$ is

$(a - b) \times (a + b) = $

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$. Which one of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module