A vector v is equally inclined to the x-axis, | vedclass

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

Question

(C) Let the vector $v$ make an angle $\alpha$ with each of the three axes. Then the direction cosines of $v$ are $\langle \cos \alpha, \cos \alpha, \c

Vedclass · Accepted Answer

$\langle \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \rangle$ or $\langle -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \rangle$

Vedclass · Answer

(C) Let the vector $v$ make an angle $\alpha$ with each of the three axes. Then the direction cosines of $v$ are $\langle \cos \alpha, \cos \alpha, \cos \alpha \rangle$. We know that for any vector,the sum of the squares of its direction cosines is $1$: $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$ $3 \cos^2 \alpha = 1$ $\cos^2 \alpha = \frac{1}{3}$ $\cos \alpha = \pm \frac{1}{\sqrt{3}}$ Therefore,the direction cosines are $\langle \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \rangle$ or $\langle -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \rangle$.

$A$ vector $v$ is equally inclined to the $x$-axis,$y$-axis,and $z$-axis respectively. Its direction cosines are:

Similar Questions

If the direction ratios $(l, m, n)$ of two lines satisfy the equations $l+m+n=0$ and $mn-2ln+lm=0$,then the angle between the lines is

In three-dimensional space,a line $AB$ makes angles of $45^\circ$ and $120^\circ$ with the positive $x$-axis and $y$-axis,respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$-axis,then $\theta = \dots^\circ$.

Write the direction ratios of the vector $\vec{a} = \hat{i} + \hat{j} - 2\hat{k}$ and hence calculate its direction cosines.

If $\theta$ is the acute angle between the two lines whose direction cosines are connected by the relations $l+m+n=0$ and $2lm+2nl-mn=0$,then $\cos \theta=$

If $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are direction cosines of $OA$ and $OB$ such that $\angle AOB = \theta$,where $O$ is the origin,then the direction cosines of the internal angular bisector of $\angle AOB$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module