If a line makes angles tan ^{-1} sqrt{7} and | vedclass

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

Question

(D) Let the angles made by the line with the $X$,$Y$,and $Z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively. Given: $\alpha = 	an ^{-1} \sqrt{7}

Vedclass · Accepted Answer

$\frac{\pi}{4}$ or $\frac{3 \pi}{4}$

Vedclass · Answer

(D) Let the angles made by the line with the $X$,$Y$,and $Z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively. Given: $\alpha = 	an ^{-1} \sqrt{7} \implies 	an \alpha = \sqrt{7}$. Since $\sec^2 \alpha = 1 + 	an^2 \alpha = 1 + 7 = 8$,we have $\cos^2 \alpha = \frac{1}{8}$. $\beta = 	an ^{-1} \frac{\sqrt{5}}{\sqrt{3}} \implies 	an \beta = \frac{\sqrt{5}}{\sqrt{3}}$. Since $\sec^2 \beta = 1 + 	an^2 \beta = 1 + \frac{5}{3} = \frac{8}{3}$,we have $\cos^2 \beta = \frac{3}{8}$. We know that $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$. Substituting the values: $\frac{1}{8} + \frac{3}{8} + \cos^2 \gamma = 1$ $\frac{4}{8} + \cos^2 \gamma = 1$ $\frac{1}{2} + \cos^2 \gamma = 1$ $\cos^2 \gamma = \frac{1}{2}$ $\cos \gamma = \pm \frac{1}{\sqrt{2}}$ Thus,$\gamma = \frac{\pi}{4}$ or $\gamma = \pi - \frac{\pi}{4} = \frac{3\pi}{4}$.

If a line makes angles $\tan ^{-1} \sqrt{7}$ and $\tan ^{-1} \frac{\sqrt{5}}{\sqrt{3}}$ with the $X$-axis and $Y$-axis respectively,then the angle made by it with the $Z$-axis is

Similar Questions

The dipole moment order of which of the following pairs of molecules is $NOT$ correct?

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\frac{g}{8}$,then the ratio of the masses is

What is the order of reactivity of halogen acids with $C_2H_5OH$?

Electric potential at an equatorial point of a small dipole with dipole moment $P$ ($r$,distance from the dipole) is

Which of the following reactions can produce aniline as the main product?

Vedclass Test Series

Exam Paper Generator

Online Exam Module