If a line makes an angle of pi /4 with the po | vedclass

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

Question

(D) Let the direction cosines of the line be $(l, m, n)$.Given that the line makes an angle of $\alpha = \pi /4$ with the $x$-axis and $\beta = \pi /4

Vedclass · Accepted Answer

$\pi /2$

Vedclass · Answer

(D) Let the direction cosines of the line be $(l, m, n)$.Given that the line makes an angle of $\alpha = \pi /4$ with the $x$-axis and $\beta = \pi /4$ with the $y$-axis.Thus,$l = \cos(\pi /4) = 1/\sqrt{2}$ and $m = \cos(\pi /4) = 1/\sqrt{2}$.We know the identity for direction cosines: $l^2 + m^2 + n^2 = 1$.Substituting the values: $(1/\sqrt{2})^2 + (1/\sqrt{2})^2 + n^2 = 1$.$1/2 + 1/2 + n^2 = 1$.$1 + n^2 = 1 \implies n^2 = 0 \implies n = 0$.If $n = \cos(\gamma) = 0$,then $\gamma = \pi /2$.Therefore,the line makes an angle of $\pi /2$ with the positive direction of the $z$-axis.

If a line makes an angle of $\pi /4$ with the positive direction of both the $x$-axis and $y$-axis,what angle does it make with the positive direction of the $z$-axis?

Similar Questions

The direction cosines of the vector joining point $A$ to point $B$,where the coordinates are $A(1, 2, -3)$ and $B(-1, -2, 1)$,are . . . . . . .

If $\theta$ is the angle between the lines $AB$ and $CD$,then the projection of line segment $AB$ on line $CD$ is:

If the coordinates of $A$ and $B$ are $(1, 2, 3)$ and $(7, 8, 7)$,then the projections of the line segment $AB$ on the coordinate axes are:

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes and $\cos \alpha = 14/15, \cos \beta = 1/3$,then $\cos \gamma = \dots$

$A$ ray makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$ and $Z$-axes respectively. Then,the value of the sine of the angle made by the ray with $X$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module