Given overrightarrow A = 3hat i + hat j + 2ha | vedclass

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

Question

(C) The unit vector $\hat n$ perpendicular to both $\overrightarrow A$ and $\overrightarrow B$ is given by $\hat n = \pm \frac{\overrightarrow A 	ime

Vedclass · Accepted Answer

Both $(a)$ and $(b)$

Vedclass · Answer

(C) The unit vector $\hat n$ perpendicular to both $\overrightarrow A$ and $\overrightarrow B$ is given by $\hat n = \pm \frac{\overrightarrow A 	imes \overrightarrow B}{|\overrightarrow A 	imes \overrightarrow B|}$.First,calculate the cross product $\overrightarrow A 	imes \overrightarrow B$:$\overrightarrow A 	imes \overrightarrow B = \begin{vmatrix} \hat i & \hat j & \hat k \ 3 & 1 & 2 \ 2 & -2 & 4 \end{vmatrix} = \hat i(4 - (-4)) - \hat j(12 - 4) + \hat k(-6 - 2) = 8\hat i - 8\hat j - 8\hat k$.Next,calculate the magnitude $|\overrightarrow A 	imes \overrightarrow B|$:$|\overrightarrow A 	imes \overrightarrow B| = \sqrt{8^2 + (-8)^2 + (-8)^2} = \sqrt{64 + 64 + 64} = \sqrt{192} = 8\sqrt{3}$.Finally,the unit vector is $\hat n = \pm \frac{8\hat i - 8\hat j - 8\hat k}{8\sqrt{3}} = \pm \frac{1}{\sqrt{3}}(\hat i - \hat j - \hat k)$.Thus,both options $(a)$ and $(b)$ are correct.

Given $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,find the unit vector perpendicular to both.

Similar Questions

Obtain the scalar product of two vectors in terms of their Cartesian components.

$\overrightarrow A = 2\hat i + 4\hat j + 4\hat k$ and $\overrightarrow B = 4\hat i + 2\hat j - 4\hat k$ are two vectors. The angle between them will be ........ $^o$.

If $\vec{A} + \vec{B} + \vec{C} = 0$,then $\vec{A} \times \vec{B}$ is equal to:

If $\overrightarrow{A} = a_{1} \hat{\imath} + a_{2} \hat{\jmath}$ and $\overrightarrow{B} = b_{1} \hat{\imath} + b_{2} \hat{\jmath}$ are perpendicular to each other,then:

If the vectors $\vec P = a\hat i + a\hat j + 3\hat k$ and $\vec Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other,then the positive value of $a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module