Find the unit vector perpendicular to the two | vedclass

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

Question

(B) Let $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.To find a vector perpendicular to both $\vec{A}$ and $\vec

Vedclass · Accepted Answer

$\frac{-\hat{i} + \hat{k}}{\sqrt{2}}$

Vedclass · Answer

(B) Let $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.To find a vector perpendicular to both $\vec{A}$ and $\vec{B}$,we calculate their cross product $\vec{C} = \vec{A} 	imes \vec{B}$.$\vec{C} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -1 & 1 \ 1 & 1 & 1 \end{vmatrix} = \hat{i}(-1 - 1) - \hat{j}(1 - 1) + \hat{k}(1 - (-1)) = -2\hat{i} + 2\hat{k}$.The magnitude of $\vec{C}$ is $|\vec{C}| = \sqrt{(-2)^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$.The unit vector $\hat{n}$ perpendicular to both is $\hat{n} = \pm \frac{\vec{C}}{|\vec{C}|} = \pm \frac{-2\hat{i} + 2\hat{k}}{2\sqrt{2}} = \pm \frac{-\hat{i} + \hat{k}}{\sqrt{2}}$.Comparing this with the given options,the correct choice is $\frac{-\hat{i} + \hat{k}}{\sqrt{2}}$.

Find the unit vector perpendicular to the two vectors $\vec{A} = \hat{i} - \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + \hat{j} + \hat{k}$.

Similar Questions

The area of the parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

What is the unit vector perpendicular to the vectors $2\hat i + 2\hat j - \hat k$ and $6\hat i - 3\hat j + 2\hat k$?

Consider two vectors $\vec{F}_1 = 2\hat{i} + 5\hat{k}$ and $\vec{F}_2 = 3\hat{j} + 4\hat{k}$. The magnitude of the scalar product of these vectors is

State and explain the characteristics of the vector product of two vectors.

An ant starts from the origin and crawls $10 \ cm$ along the $x$-axis and then $20 \ cm$ along the $y$-axis. The dot product of the ant's displacement vector with the position vector of a point that makes $45^{\circ}$ with the $x$-axis and has a magnitude of $\sqrt{2} \ cm$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module