CUET · MATHS · PYQ PAPER 2023
Equation of a line is \(\frac{x-3}{2}=\frac{4-y}{3}=\frac{2-z}{4}\) then its direction cosines are:
- A 2, 3, 4
- B \(2,-3,-4\)
- C \(\frac{2}{29},-\frac{3}{29},-\frac{4}{29}\)
- D \(\frac{2}{\sqrt{29}},-\frac{3}{\sqrt{29}},-\frac{4}{\sqrt{29}}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{\sqrt{29}},-\frac{3}{\sqrt{29}},-\frac{4}{\sqrt{29}}\)
Step-by-step Solution
Detailed explanation
Equation of line: \(\frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-2}{-4}\) Direction ratios: \(a=2, b=-3, c=-4\) Magnitude: \(\sqrt{a^2+b^2+c^2} = \sqrt{2^2+(-3)^2+(-4)^2} = \sqrt{4+9+16} = \sqrt{29}\) Direction cosines:…
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