What vector must be added to the two vectors | vedclass

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

Question

(B) Let the required vector be $\vec{R}$.According to the problem,the sum of the given vectors and $\vec{R}$ is equal to the unit vector along the $X$

Vedclass · Accepted Answer

$-2\hat{i} + \hat{j} - \hat{k}$

Vedclass · Answer

(B) Let the required vector be $\vec{R}$.According to the problem,the sum of the given vectors and $\vec{R}$ is equal to the unit vector along the $X$-axis,which is $\hat{i}$.$(\hat{i} - 2\hat{j} + 2\hat{k}) + (2\hat{i} + \hat{j} - \hat{k}) + \vec{R} = \hat{i}$Combine the given vectors:$(1+2)\hat{i} + (-2+1)\hat{j} + (2-1)\hat{k} + \vec{R} = \hat{i}$$3\hat{i} - \hat{j} + \hat{k} + \vec{R} = \hat{i}$Now,solve for $\vec{R}$:$\vec{R} = \hat{i} - (3\hat{i} - \hat{j} + \hat{k})$$\vec{R} = \hat{i} - 3\hat{i} + \hat{j} - \hat{k}$$\vec{R} = -2\hat{i} + \hat{j} - \hat{k}$

What vector must be added to the two vectors $\hat{i} - 2\hat{j} + 2\hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$ so that the resultant may be a unit vector along the $X$-axis?

Similar Questions

The magnitudes of vectors $\vec A, \vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$,the angle between $\vec A$ and $\vec B$ is

$A$ particle moves $21 \ m$ along the direction of the vector $6\hat{i} + 2\hat{j} + 3\hat{k}$,then it moves $14 \ m$ along the direction of the vector $3\hat{i} - 2\hat{j} + 6\hat{k}$. What is its total displacement (in meters)?

$A$ football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled,the new resultant vector is perpendicular to $\vec{P}$. What is the magnitude of $\vec{R}$?

Two forces whose magnitudes are in the ratio $5:3$ are acting at a point at an angle $60^{\circ}$ simultaneously. If the resultant of the two forces is $35 \ N$,then the magnitudes of the two forces respectively are

Vedclass Test Series

Exam Paper Generator

Online Exam Module