Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If a line makes angles $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $X, Y$ and $Z$ axis respectively, then its direction cosines are
MathematicsThree Dimensional GeometryAP EAMCETAP EAMCET 2021 (23 Aug Shift 2)
Options:
  • A $\left(0, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)$
  • B $\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
  • C $\left(1, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
  • D $\left(1, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
Solution:
1664 Upvotes Verified Answer
The correct answer is: $\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
Given, a line makes $90^{\circ}, 135^{\circ}$ and $45^{\circ}$ with the positive $x, y$ and $z$ axes respectively.
Hence, it's direction cosines are
$ < \cos 90^{\circ}, \cos 135^{\circ}, \cos 45^{\circ}>$
$=\left(0, \frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.