If a = 2 hat{i} + 3 hat{j} - hat{k},b = hat{i | vedclass

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

Question

(D) vector that lies in the plane of $b$ and $c$ is given by a linear combination of $b$ and $c$. $A$ vector perpendicular to $a$ and lying in the pla

Vedclass · Accepted Answer

$-17 \hat{i} - 21 \hat{j} - 97 \hat{k}$

Vedclass · Answer

(D) vector that lies in the plane of $b$ and $c$ is given by a linear combination of $b$ and $c$. $A$ vector perpendicular to $a$ and lying in the plane of $b$ and $c$ is given by the vector product $a 	imes (b 	imes c)$.First,we calculate $b 	imes c$:$b 	imes c = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & 2 & -5 \ 3 & 5 & -1 \end{vmatrix} = \hat{i}(-2 + 25) - \hat{j}(-1 + 15) + \hat{k}(5 - 6) = 23 \hat{i} - 14 \hat{j} - \hat{k}$.Now,we calculate $a 	imes (b 	imes c)$:$a 	imes (b 	imes c) = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 3 & -1 \ 23 & -14 & -1 \end{vmatrix} = \hat{i}(-3 - 14) - \hat{j}(-2 + 23) + \hat{k}(-28 - 69) = -17 \hat{i} - 21 \hat{j} - 97 \hat{k}$.Thus,the required vector is $-17 \hat{i} - 21 \hat{j} - 97 \hat{k}$.

If $a = 2 \hat{i} + 3 \hat{j} - \hat{k}$,$b = \hat{i} + 2 \hat{j} - 5 \hat{k}$,and $c = 3 \hat{i} + 5 \hat{j} - \hat{k}$,then a vector perpendicular to $a$ and in the plane containing $b$ and $c$ is:

Similar Questions

If $\bar{a} = 4\hat{i} + 3\hat{j} + \hat{k}$ and $\bar{b} = \hat{i} - 2\hat{j} + 2\hat{k}$,then find the value of $\bar{a} \times (\bar{a} \times (\bar{a} \times (\bar{a} \times \bar{b})))$.

The position vectors of the points $A, B$ and $C$ are $i + j, j + k$ and $k + i$ respectively. The vector area of the $\Delta ABC = \pm \frac{1}{2} \vec{\alpha}$ where $\vec{\alpha} = $

The number of unit vectors perpendicular to $\overline{a}=(1,1,0)$ and $\overline{b}=(0,1,1)$ is

Let $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ be the position vectors of the vertices $A, B, C$ respectively of $\triangle ABC$. The vector area of $\triangle ABC$ is:

Let $\vec{a}=2\hat{i}-5\hat{j}+5\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+3\hat{k}$. If $\vec{c}$ is a vector such that $2(\vec{a}\times\vec{c})+3(\vec{b}\times\vec{c})=\vec{0}$ and $(\vec{a}-\vec{b})\cdot\vec{c}=-97$, then $|\vec{c}\times \hat{k}|^{2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module