What is the unit vector perpendicular to the | vedclass

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

Question

(C) Let $\vec A = 2\hat i + 2\hat j - \hat k$ and $\vec B = 6\hat i - 3\hat j + 2\hat k$.The vector perpendicular to both $\vec A$ and $\vec B$ is giv

Vedclass · Accepted Answer

$\frac{\hat i - 10\hat j - 18\hat k}{5\sqrt{17}}$

Vedclass · Answer

(C) Let $\vec A = 2\hat i + 2\hat j - \hat k$ and $\vec B = 6\hat i - 3\hat j + 2\hat k$.The vector perpendicular to both $\vec A$ and $\vec B$ is given by their cross product $\vec C = \vec A 	imes \vec B$.$\vec C = \begin{vmatrix} \hat i & \hat j & \hat k \ 2 & 2 & -1 \ 6 & -3 & 2 \end{vmatrix} = \hat i(4 - 3) - \hat j(4 + 6) + \hat k(-6 - 12) = \hat i - 10\hat j - 18\hat k$.The unit vector $\hat n$ is given by $\frac{\vec C}{|\vec C|}$.$|\vec C| = \sqrt{1^2 + (-10)^2 + (-18)^2} = \sqrt{1 + 100 + 324} = \sqrt{425} = \sqrt{25 	imes 17} = 5\sqrt{17}$.Therefore,$\hat n = \frac{\hat i - 10\hat j - 18\hat k}{5\sqrt{17}}$.

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

Similar Questions

Two vectors $\vec{P}$ and $\vec{Q}$ are at an angle $\theta$ to each other. Which of the following is a unit vector perpendicular to both $\vec{P}$ and $\vec{Q}$?

The angle between vectors $(\overrightarrow {A} \times \overrightarrow {B})$ and $(\overrightarrow {B} \times \overrightarrow {A})$ is

Show that the scalar product of two vectors obeys the commutative law.

If the vectors $2\hat{i} + 2\hat{j} - 2\hat{k}$,$5\hat{i} + y\hat{j} + \hat{k}$,and $-\hat{i} + 2\hat{j} + 2\hat{k}$ are coplanar,then the value of $y$ is:

If $\vec A = 2\hat i + \hat j - \hat k$,$\vec B = \hat i + 2\hat j + 3\hat k$ and $\vec C = 6\hat i - 2\hat j - 6\hat k$,then the angle between $(\vec A + \vec B)$ and $\vec C$ will be ....... $^o$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module