A vector overrightarrow{A} when added to the | vedclass

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

Question

(B) Let the given vectors be $\vec{B} = (\hat{\imath}-2 \hat{\jmath}+2 \hat{k})$ and $\vec{C} = (-2 \hat{\imath}+\hat{\jmath}-\hat{k})$.The sum of the

Vedclass · Accepted Answer

$\sqrt{6}$

Vedclass · Answer

(B) Let the given vectors be $\vec{B} = (\hat{\imath}-2 \hat{\jmath}+2 \hat{k})$ and $\vec{C} = (-2 \hat{\imath}+\hat{\jmath}-\hat{k})$.The sum of these vectors is $\vec{B} + \vec{C} = (1-2)\hat{\imath} + (-2+1)\hat{\jmath} + (2-1)\hat{k} = -\hat{\imath} - \hat{\jmath} + \hat{k}$.According to the problem,$\vec{A} + (\vec{B} + \vec{C}) = \hat{\jmath}$ (unit vector along the $y$-axis).Substituting the sum: $\vec{A} + (-\hat{\imath} - \hat{\jmath} + \hat{k}) = \hat{\jmath}$.Solving for $\vec{A}$: $\vec{A} = \hat{\jmath} - (-\hat{\imath} - \hat{\jmath} + \hat{k}) = \hat{\jmath} + \hat{\imath} + \hat{\jmath} - \hat{k} = \hat{\imath} + 2\hat{\jmath} - \hat{k}$.The magnitude of $\vec{A}$ is $|\vec{A}| = \sqrt{(1)^2 + (2)^2 + (-1)^2} = \sqrt{1 + 4 + 1} = \sqrt{6}$.

$A$ 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

Similar Questions

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{R_1}$. If vector $\vec{B}$ is reversed,the resultant becomes $\vec{R_2}$. What is the value of $R_1^2 + R_2^2$?

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:

The ratio of the maximum and minimum magnitudes of the resultant of two vectors $\vec{a}$ and $\vec{b}$ is $3 : 1$. Then $|\vec{a}|$ is equal to:

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

Two forces are such that the sum of their magnitudes is $18 \,N$ and their resultant is perpendicular to the smaller force and the magnitude of the resultant is $12 \,N$. Then the magnitudes of the forces are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module