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

The unit vector parallel to the resultant of vectors $\vec{A} = 4\hat{i} - 3\hat{j}$ and $\vec{B} = 8\hat{i} + 8\hat{j}$ is:

Find the magnitude and direction of the resultant of two vectors $A$ and $B$ in terms of their magnitudes and the angle $\theta$ between them.

Two forces,each numerically equal to $10$ $dyne$,are acting as shown in the adjoining figure. The magnitude of the resultant force is ......... $dyne$.

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$ respectively. Find the angle made by the resultant vector with the $X$-axis.

If the magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector, then find the angle between the two vectors in degrees $(^{\circ})$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module