If a line makes angles frac{pi}{4} and frac{p | vedclass

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

Question

(B) Let the line make angles $\alpha, \beta, \gamma$ with the $X, Y, Z$-axes respectively. The direction cosines are $l = \cos \alpha, m = \cos \beta,

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(B) Let the line make angles $\alpha, \beta, \gamma$ with the $X, Y, Z$-axes respectively. The direction cosines are $l = \cos \alpha, m = \cos \beta, n = \cos \gamma$. Given $\beta = \frac{\pi}{4}$ and $\gamma = \frac{\pi}{3}$. We know that $l^2 + m^2 + n^2 = 1$. Substituting the values: $\cos^2 \alpha + \cos^2 \frac{\pi}{4} + \cos^2 \frac{\pi}{3} = 1$. $\cos^2 \alpha + (\frac{1}{\sqrt{2}})^2 + (\frac{1}{2})^2 = 1$. $\cos^2 \alpha + \frac{1}{2} + \frac{1}{4} = 1$. $\cos^2 \alpha + \frac{3}{4} = 1 \Rightarrow \cos^2 \alpha = \frac{1}{4}$. $\cos \alpha = \pm \frac{1}{2}$. Since the angle $\alpha$ is obtuse,$\cos \alpha$ must be negative,so $\cos \alpha = -\frac{1}{2}$. Therefore,$\alpha = \pi - \frac{\pi}{3} = \frac{2 \pi}{3}$.

If a line makes angles $\frac{\pi}{4}$ and $\frac{\pi}{3}$ with $Y$-axis and $Z$-axis respectively,then the obtuse angle made by that line with $X$-axis is

Similar Questions

The projection of a line segment on the coordinate axes are $3, 4,$ and $5$ respectively. Find the length of the line segment.

$A$ point $(x, y, z)$ moves parallel to the $xy$-plane. Which of the three variables $x, y, z$ remains fixed?

If a directed line makes angles $45^{\circ}$ and $60^{\circ}$ with the $X$ and $Y$-axes respectively,then the obtuse angle $\theta$ made by the line with the $Z$-axis is (in $^{\circ}$)

The coordinates of the point $P$ are $(x, y, z)$ and the direction cosines of the line $OP$ where $O$ is the origin $(0, 0, 0)$ are $l, m, n$. If $r$ is the distance $OP$,then which of the following relations is correct?

If the direction ratios of two lines are $5, -12, 13$ and $-3, 4, 5$,then the angle between them is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module