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

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

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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 $\vec{a}=-5 \hat{i}+\hat{j}-3 \hat{k}$,$\vec{b}=\hat{i}+2 \hat{j}-4 \hat{k}$ and $\vec{c}=(((\vec{a} \times \vec{b}) \times \hat{i}) \times \hat{i}) \times \hat{i}$. Then $\vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k})$ is equal to

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$,$\vec{b}=-\hat{i}+2\hat{j}-2\hat{k}$ and $\vec{c}=2\hat{i}-\hat{j}+2\hat{k}$,then $(\vec{a}-\vec{b}) \cdot [(\vec{a} \times \vec{b}) \times (\vec{a} \times \vec{c})]$ is

$a \times (b \times c)$ is equal to

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 $\vec{a}, \vec{b}, \vec{c}$ are three vectors of magnitudes $\sqrt{3}, 1, 2$ respectively,such that $\vec{a} \times (\vec{a} \times \vec{c}) + 3\vec{b} = \vec{0}$. If $\theta$ is the angle between $\vec{a}$ and $\vec{c}$,then $\cos^2 \theta = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module