Let a=hat{i}+2 hat{j}-hat{k} and b=hat{i}+hat | vedclass

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

Question

(C) Given vectors are $a=\hat{i}+2 \hat{j}-\hat{k}$ and $b=\hat{i}+\hat{j}+\hat{k}$.First, we calculate the cross product $a 	imes b$:$a 	imes b = \

Vedclass · Accepted Answer

$\frac{1}{\sqrt{14}}(3 \hat{i}-2 \hat{j}-\hat{k})$

Vedclass · Answer

(C) Given vectors are $a=\hat{i}+2 \hat{j}-\hat{k}$ and $b=\hat{i}+\hat{j}+\hat{k}$.First, we calculate the cross product $a 	imes b$:$a 	imes b = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 2 & -1 \ 1 & 1 & 1 \end{vmatrix} = \hat{i}(2 - (-1)) - \hat{j}(1 - (-1)) + \hat{k}(1 - 2) = 3\hat{i} - 2\hat{j} - \hat{k}$.The scalar triple product is defined as $[a b p] = p \cdot (a 	imes b)$.Since $p$ is a unit vector, $|p| = 1$. Let $	heta$ be the angle between $p$ and $(a 	imes b)$.Then $[a b p] = |p| |a 	imes b| \cos 	heta = |a 	imes b| \cos 	heta$.This expression is maximum when $\cos 	heta = 1$, which means $p$ must be in the same direction as $(a 	imes b)$.Thus, $p = \frac{a 	imes b}{|a 	imes b|} = \frac{3\hat{i} - 2\hat{j} - \hat{k}}{\sqrt{3^2 + (-2)^2 + (-1)^2}} = \frac{1}{\sqrt{14}}(3\hat{i} - 2\hat{j} - \hat{k})$.

Let $a=\hat{i}+2 \hat{j}-\hat{k}$ and $b=\hat{i}+\hat{j}+\hat{k}$. If $p$ is a unit vector such that $[a b p]$ is maximum, then $p=$

Similar Questions

$A$ unit vector coplanar with $i+j+3k$ and $i+3j+k$ and perpendicular to $i+j+k$ is

If $a, b, c$ are vectors such that $[a, b, c] = 4$,then $[a \times b, b \times c, c \times a] = $

If $[\bar{a} \quad \bar{b} \quad \bar{c}]=4$,then the volume of the parallelepiped with coterminous edges $\bar{a}+2 \bar{b}$,$\bar{b}+2 \bar{c}$,and $\bar{c}+2 \bar{a}$ is:

The volume of the tetrahedron having the edges $\hat{i}+2\hat{j}-\hat{k}$, $\hat{i}+\hat{j}+\hat{k}$, and $\hat{i}-\hat{j}+\lambda\hat{k}$ as coterminous edges is $\frac{2}{3}$ cubic units. Then $\lambda$ equals:

If $\vec a = 2\sin \theta \hat i - \hat j + 2\hat k$,$\vec b = 2\hat i + 2\sin \theta \hat j - \hat k$ and $\vec c = 4\hat i + \hat j + 4\cos^2 \theta \hat k$ are coplanar,then $\theta$ can be equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module