If bar{a} is perpendicular to bar{b} and bar{ | vedclass

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

Question

(D) The scalar triple product is defined as $\left[\bar{a} \bar{b} \bar{c}ight] = \bar{a} \cdot (\bar{b} 	imes \bar{c})$.Since $\bar{a}$ is perpend

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) The scalar triple product is defined as $\left[\bar{a} \bar{b} \bar{c}ight] = \bar{a} \cdot (\bar{b} 	imes \bar{c})$.Since $\bar{a}$ is perpendicular to both $\bar{b}$ and $\bar{c}$,$\bar{a}$ must be parallel to the vector $\bar{b} 	imes \bar{c}$.Let $\hat{n}$ be the unit vector perpendicular to $\bar{b}$ and $\bar{c}$. Then $\bar{b} 	imes \bar{c} = |\bar{b}||\bar{c}| \sin\left(\frac{\pi}{3}ight) \hat{n} = 3 	imes 4 	imes \frac{\sqrt{3}}{2} \hat{n} = 6\sqrt{3} \hat{n}$.Since $\bar{a}$ is perpendicular to $\bar{b}$ and $\bar{c}$,$\bar{a} = |\bar{a}| \hat{n} = 2 \hat{n}$.Therefore,$\left[\bar{a} \bar{b} \bar{c}ight] = \bar{a} \cdot (\bar{b} 	imes \bar{c}) = (2 \hat{n}) \cdot (6\sqrt{3} \hat{n}) = 12\sqrt{3} (\hat{n} \cdot \hat{n}) = 12\sqrt{3} 	imes 1 = 12\sqrt{3}$.

If $\bar{a}$ is perpendicular to $\bar{b}$ and $\bar{c}$,$|\vec{a}|=2$,$|\bar{b}|=3$,$|\bar{c}|=4$ and the angle between $\bar{b}$ and $\bar{c}$ is $\frac{\pi}{3}$,then $\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]=$ (in $\sqrt{3}$)

Similar Questions

If the vectors $\vec{b}, \vec{c}, \vec{d}$ are not coplanar, then the vector $(\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d})+(\vec{a} \times \vec{c}) \times(\vec{d} \times \vec{b})+(\vec{a} \times \vec{d}) \times(\vec{b} \times \vec{c})$ is

If the vectors $\vec{a} = \hat{i} + a\hat{j} + \hat{k}$,$\vec{b} = \hat{j} + a\hat{k}$,and $\vec{c} = a\hat{i} + \hat{k}$ are given,find the value of $a$ for which the volume of the parallelepiped formed by these three vectors as coterminous edges is minimum.

The volume of the tetrahedron formed by the vectors $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is:

If $a = 3i - 2j + 2k$,$b = 6i + 4j - 2k$ and $c = 3i - 2j - 4k$,then $a \cdot (b \times c)$ is

Let $a=2 \hat{i}+\hat{j}-3 \hat{k}$ and $b=\hat{i}+3 \hat{j}+2 \hat{k}$. Then the volume of the parallelopiped having coterminous edges as $a, b$ and $c$, where $c$ is the vector perpendicular to the plane of $a, b$ and $|c|=2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module