MHT CET · Maths · Three Dimensional Geometry
f a line in octant OXYZ makes equal angles with co-ordinate axes, then
- A \(l=m=n=\frac{1}{3}\)
- B \(l=m=n=-\frac{1}{3}\)
- C \(l=m=n=\frac{1}{\sqrt{3}}\)
- D \(l=m=n=-\frac{1}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(l=m=n=\frac{1}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Let the direction cosines of the lines makes an angle \(\alpha\) with each of coordinate axes.
\(\therefore \ell+\mathrm{m}^{2}+\mathrm{n}^{2}=1\)
\(\therefore 3 \cos ^{2} \alpha=1 \Rightarrow \cos ^{2} \alpha=\frac{1}{3} \Rightarrow \cos \alpha=\pm \frac{1}{\sqrt{3}} \Rightarrow \ell=\) \(\mathrm{m}\) \(=\mathrm{n}=\frac{1}{\sqrt{3}}\)
\(\therefore \ell+\mathrm{m}^{2}+\mathrm{n}^{2}=1\)
\(\therefore 3 \cos ^{2} \alpha=1 \Rightarrow \cos ^{2} \alpha=\frac{1}{3} \Rightarrow \cos \alpha=\pm \frac{1}{\sqrt{3}} \Rightarrow \ell=\) \(\mathrm{m}\) \(=\mathrm{n}=\frac{1}{\sqrt{3}}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Three vectors \(\hat{i}-\hat{\mathrm{k}}, \lambda \hat{i}+\hat{\mathrm{j}}+(1-\lambda) \hat{\mathrm{k}}\) and \(\mu \hat{i}+\lambda \hat{\mathrm{j}}+(1+\lambda-\mu) \hat{\mathrm{k}}\) represents conterminus edges of a parallelopiped, then the volume of the parallelopiped depends on.MHT CET 2025 Medium
- A parents has two children. If one of them is boy, then the probability that other is, also a boy, isMHT CET 2008 Medium
- Given three vectors \(\bar{a}, \bar{b}, \bar{c}\), two of which are collinear. If \(\bar{a}+\bar{b}\) is collinear with \(\bar{c}\) and \(\bar{b}+\bar{c}\) is collinear with \(|\bar{a}|=|\bar{b}|=|\bar{c}|=\sqrt{2}\), then \(\bar{a} \cdot \bar{b}+\bar{b} \cdot \bar{c}+\bar{c} \cdot \bar{a}=\)MHT CET 2022 Easy
- \(\int \sin ^5 x \mathrm{~d} x=\)MHT CET 2025 Medium
- In a triangle \(A B C\), with usual notations, if \(b=\sqrt{3}, c=1, \angle A=30^{\circ}\), then angle \(B\) isMHT CET 2022 Medium
- The area of the region included between the parabola \(y^{2}=x\) and the line \(x+y=2\) in the first quardrant isMHT CET 2020 Medium
More PYQs from MHT CET
- Identify the major product formed when 2-Methylhexan-3-ol is heated with concentrated sulphuric acid.
MHT CET 2024 Medium - Sometimes a pregnant woman is injected with _________ hormone to hasten parturition.MHT CET 2021 Medium
- What is total number of crystal systems associated with 14 Bravais lattices?MHT CET 2023 Easy
- If are cartesian co-ordinates of the point, then its polar co-ordinates are…..MHT CET 2019 Easy
- The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, areMHT CET 2023 Medium
- A particle of mass is moving in SHM with a path length of and frequency of . The maximum force in newton, acting on the particle isMHT CET 2018 Medium