A space vector makes the angles 150^{circ} an | vedclass

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

Question

(A) We know that for a space vector making angles $\alpha, \beta$,and $\gamma$ with the positive direction of the $x, y$,and $z$-axes respectively,the

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) We know that for a space vector making angles $\alpha, \beta$,and $\gamma$ with the positive direction of the $x, y$,and $z$-axes respectively,the direction cosines satisfy the relation: $\cos^{2} \alpha + \cos^{2} \beta + \cos^{2} \gamma = 1$ Given that $\alpha = 150^{\circ}$ and $\beta = 60^{\circ}$. Substituting these values into the equation: $\cos^{2} 150^{\circ} + \cos^{2} 60^{\circ} + \cos^{2} \gamma = 1$ Since $\cos 150^{\circ} = -\frac{\sqrt{3}}{2}$ and $\cos 60^{\circ} = \frac{1}{2}$,we have: $(-\frac{\sqrt{3}}{2})^{2} + (\frac{1}{2})^{2} + \cos^{2} \gamma = 1$ $\frac{3}{4} + \frac{1}{4} + \cos^{2} \gamma = 1$ $1 + \cos^{2} \gamma = 1$ $\cos^{2} \gamma = 0$ $\cos \gamma = 0$ Therefore,$\gamma = 90^{\circ}$.

$A$ space vector makes the angles $150^{\circ}$ and $60^{\circ}$ with the positive direction of $x$- and $y$-axes. The angle made by the vector with the positive direction of the $z$-axis is (in $^{\circ}$)

Similar Questions

Fill in the blanks:
Coordinate planes divide the space into ........ octants.

If the direction cosines of a line are $\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$ and $c-a=4$,then $ca=$

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with $y$ and $z$-axes,respectively.

If the direction ratios of a line are proportional to $1, 2, 3$,find the projection of the line segment joining the points $(5, 2, 3)$ and $(-1, 0, 2)$ on the line.

The angle between the lines with direction ratios $(2, -2, 1)$ and $(1, -2, 2)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module