Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

If a line makes an angle of $\pi /4$ with the positive directions of each of $x$ -axis and $y$ -axis, then the angle that the line makes with the positive direction of the $z$ -axis is

Option 1)
$\pi /4$

Option 2)
$\pi / 3$

Option 3)
$\pi / 2$

Option 4)
$\pi /6$

Answers (1)

best_answer

As we have learned

Direction Cosines -

If $\alpha, \beta, \gamma$ are the angles which a vector makes with positive X-axis,Y-axis and Z-axis respectively then $\cos \alpha, \cos \beta, \cos \gamma$ are known as diresction cosines, generally denoted by (l,m,n).

$l=\cos \alpha, m=\cos \beta, n=\cos \gamma$

$l^{2}+m^{2}+n^{2}= 1$

$\cos^{2} \alpha+ \cos^{2} \beta+\cos^{2} \gamma= 1$

- wherein

$l =\cos \alpha = \cos \frac{\pi }{4}= 1/ \sqrt 2$

$m = \cos \beta = \cos \pi /4 = 1/ \sqrt 2$

Now ,

$l ^ 2 + m^2 + n^2 = 1$

$\Rightarrow n^2 = 1- (1/2 + 1/2 ) = 0$

$\cos Y = 0$

$Y = \pi /2$

Option 3 is correct.

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2

anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question