If three vectors along coordinate axes repres | vedclass

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

Question

(D) The three vectors along the coordinate axes representing the adjacent sides of a cube of length $b$ are $b\hat{i}$,$b\hat{j}$,and $b\hat{k}$.The d

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The three vectors along the coordinate axes representing the adjacent sides of a cube of length $b$ are $b\hat{i}$,$b\hat{j}$,and $b\hat{k}$.The diagonal vector $\vec{A}$ passing through the origin is the resultant of these three vectors: $\vec{A} = b\hat{i} + b\hat{j} + b\hat{k}$.The magnitude of this diagonal vector is $|\vec{A}| = \sqrt{b^2 + b^2 + b^2} = \sqrt{3b^2} = b\sqrt{3}$.The unit vector $\hat{A}$ along the diagonal is given by $\hat{A} = \frac{\vec{A}}{|\vec{A}|} = \frac{b\hat{i} + b\hat{j} + b\hat{k}}{b\sqrt{3}} = \frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}$.

If three vectors along coordinate axes represent the adjacent sides of a cube of length $b$,then the unit vector along its diagonal passing through the origin will be

Similar Questions

If $|\vec A + \vec B| = |\vec A| + |\vec B|$,then the angle between $\vec A$ and $\vec B$ will be ....... $^o$.

Three forces of $3 \ N$,$4 \ N$,and $12 \ N$ act on a point in mutually perpendicular directions. The magnitude of the resultant force is ........ $N$.

Which of the following relations is correct?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to vector $\vec{A}$,and the resultant magnitude is equal to half of the magnitude of $\vec{B}$. Then,the angle between $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

The angles which a vector $\hat{i} + \hat{j} + \sqrt{2} \hat{k}$ makes with $X, Y$ and $Z$ axes respectively are

Vedclass Test Series

Exam Paper Generator

Online Exam Module