A line makes a 45^{circ} angle with the posit | vedclass

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

Question

(C) Let the angles made by the line with the positive $X$,$Y$,and $Z$ axes be $\alpha$,$\beta$,and $\gamma$ respectively. Given $\alpha = 45^{\circ}$

Vedclass · Accepted Answer

$165$

Vedclass · Answer

(C) Let the angles made by the line with the positive $X$,$Y$,and $Z$ axes be $\alpha$,$\beta$,and $\gamma$ respectively. Given $\alpha = 45^{\circ}$ and $\beta = \gamma$. Using the direction cosine property $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$: $\cos^2 45^{\circ} + \cos^2 \beta + \cos^2 \beta = 1$ $\left(\frac{1}{\sqrt{2}}\right)^2 + 2\cos^2 \beta = 1$ $\frac{1}{2} + 2\cos^2 \beta = 1$ $2\cos^2 \beta = \frac{1}{2}$ $\cos^2 \beta = \frac{1}{4}$ $\cos \beta = \frac{1}{2}$ (since angles are acute) $\beta = 60^{\circ}$. Thus,$\beta = 60^{\circ}$ and $\gamma = 60^{\circ}$. The sum of the angles is $\alpha + \beta + \gamma = 45^{\circ} + 60^{\circ} + 60^{\circ} = 165^{\circ}$.

$A$ line makes a $45^{\circ}$ angle with the positive $X$-axis and makes equal angles with the positive $Y$-axis and $Z$-axis respectively. The sum of the three angles which the line makes with the positive $X$-axis,$Y$-axis,and $Z$-axis is: (in $^{\circ}$)

Similar Questions

The direction cosines of the line $\frac{x-1}{0}=\frac{y+1}{5}=\frac{z-3}{0}$ are . . . . . . .

If the relation between the direction ratios of two lines in $\mathbb{R}^3$ are given by $l+m+n=0$ and $2lm+2mn-ln=0$,then the angle between the lines is ($l, m, n$ have their usual meaning).

If the direction cosines of two lines are such that $2l + m + 2n = 0$ and $3l^2 + 5m^2 - 11n^2 = 0$,then the angle between the two lines is

$A$ line makes angles $\alpha, \beta, \gamma$ and $\delta$ with the diagonals of a cube. Prove that $\cos^{2} \alpha + \cos^{2} \beta + \cos^{2} \gamma + \cos^{2} \delta = \frac{4}{3}$.

If the direction ratios of a line are $1, -3, 2$,what are its direction cosines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module