If bar{a} and bar{b} are two vectors such tha | vedclass

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

Question

(B) Given $|\bar{a}| = |\bar{b}| = \sqrt{6}$ and $\bar{a} \cdot \bar{b} = -1$. We know that $\bar{a} \cdot \bar{b} = |\bar{a}| |\bar{b}| \cos(	heta)$

Vedclass · Accepted Answer

$35$

Vedclass · Answer

(B) Given $|\bar{a}| = |\bar{b}| = \sqrt{6}$ and $\bar{a} \cdot \bar{b} = -1$. We know that $\bar{a} \cdot \bar{b} = |\bar{a}| |\bar{b}| \cos(	heta)$. Substituting the values: $-1 = (\sqrt{6})(\sqrt{6}) \cos(	heta) = 6 \cos(	heta)$. So, $\cos(	heta) = -\frac{1}{6}$. Since $\sin^2(	heta) = 1 - \cos^2(	heta)$, we have $\sin^2(	heta) = 1 - (-\frac{1}{6})^2 = 1 - \frac{1}{36} = \frac{35}{36}$. Thus, $\sin(	heta) = \frac{\sqrt{35}}{6}$. Now, $|\bar{a} 	imes \bar{b}| = |\bar{a}| |\bar{b}| \sin(	heta) = (\sqrt{6})(\sqrt{6}) \sin(	heta) = 6 \sin(	heta)$. Therefore, $|\bar{a} 	imes \bar{b}| \sin(	heta) = 6 \sin(	heta) \cdot \sin(	heta) = 6 \sin^2(	heta) = 6 	imes \frac{35}{36} = \frac{35}{6}$.

If $\bar{a}$ and $\bar{b}$ are two vectors such that $|\bar{a}|=|\bar{b}|=\sqrt{6}$ and $\bar{a} \cdot \bar{b}=-1$, then find the value of $|\bar{a} \times \bar{b}| \sin(\theta)$, where $\theta$ is the angle between $\bar{a}$ and $\bar{b}$.

Similar Questions

Let $\vec{b}$ and $\vec{c}$ be non-collinear vectors satisfying $\vec{a} \times (\vec{b} \times \vec{c}) + (\vec{a} \cdot \vec{b})\vec{b} = (4 - 2x - \sin y)\vec{b} + (x^2 - 1)\vec{c}$ and $(\vec{c} \cdot \vec{c})\vec{a} = \vec{c}$,then $x$ is equal to

Let $\vec a, \vec b, \vec c$ be three vectors such that $\vec a \perp (\vec b + \vec c)$,$\vec b \perp (\vec c + \vec a)$,and $\vec c \perp (\vec a + \vec b)$. If $|\vec a| = 1, |\vec b| = 2, |\vec c| = 3$,then $|\vec a + \vec b + \vec c| = \dots$

Let $\vec{u}$ and $\vec{v}$ be two non-zero vectors with the intermediate angle $45^{\circ}$. Then $|\vec{u} \times \vec{v}|=$

The scalar product of the vector $\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of the vectors $2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\lambda \hat{i}+2 \hat{j}+3 \hat{k}$ is equal to $1$. Then the value of $\lambda$ is:

If $x$ and $y$ are two unit vectors and the angle between them is $\phi$,then $\frac{1}{2} |x - y| = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module