Three vectors are expressed as vec{a} = 4hat{ | vedclass

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

Question

(A) First,find the sum of the vectors $\vec{R} = \vec{a} + \vec{b} + \vec{c}$.$\vec{R} = (4\hat{i} - \hat{j}) + (-3\hat{i} + 2\hat{j}) + (-\hat{k})$$\

Vedclass · Accepted Answer

$\frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}}$

Vedclass · Answer

(A) First,find the sum of the vectors $\vec{R} = \vec{a} + \vec{b} + \vec{c}$.$\vec{R} = (4\hat{i} - \hat{j}) + (-3\hat{i} + 2\hat{j}) + (-\hat{k})$$\vec{R} = (4 - 3)\hat{i} + (-1 + 2)\hat{j} - \hat{k} = \hat{i} + \hat{j} - \hat{k}$.Next,calculate the magnitude of the resultant vector $\vec{R}$:$|\vec{R}| = \sqrt{(1)^2 + (1)^2 + (-1)^2} = \sqrt{1 + 1 + 1} = \sqrt{3}$.The unit vector $\hat{u}$ along the direction of $\vec{R}$ is given by $\hat{u} = \frac{\vec{R}}{|\vec{R}|}$.$\hat{u} = \frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}}$.

Three vectors are expressed as $\vec{a} = 4\hat{i} - \hat{j}$,$\vec{b} = -3\hat{i} + 2\hat{j}$,and $\vec{c} = -\hat{k}$. The unit vector along the direction of the sum of these vectors is:

Similar Questions

Can the resultant of $2$ vectors be zero?

Two forces of magnitudes $3 \ N$ and $4 \ N$ act on an object. If the angle between them is $180^\circ$,then their resultant force is ......... $N$.

$A$ vector $\overrightarrow{A}$ when added to the sum of the vectors $(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})$ and $(-2 \hat{\imath}+\hat{\jmath}-\hat{k})$ gives a unit vector along the $y$-axis. The magnitude of the vector $\overrightarrow{A}$ is

If $\overrightarrow{A} = 3\widehat{i} + 2\widehat{j}$ and $\overrightarrow{B} = \widehat{i} + \widehat{j} - 2\widehat{k}$,find their sum using the algebraic method.

Three vectors each of magnitude $3 \sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$,then the magnitude of the resultant vector of the three vectors is

Vedclass Test Series

Exam Paper Generator

Online Exam Module