CUET · MATHS · PYQ PAPER 2023
A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
Direction cosines of the line passing through the points \(A\) and \(B\) are:
- A \(\frac{2}{\sqrt{38}}, \frac{3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\)
- B \(\frac{2}{\sqrt{38}},-\frac{3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\)
- C \(-\frac{2}{\sqrt{38}},-\frac{3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\)
- D \(-\frac{2}{\sqrt{38}}, \frac{3}{\sqrt{38}},-\frac{5}{\sqrt{38}}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{\sqrt{38}},-\frac{3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\)
Step-by-step Solution
Detailed explanation
Direction ratios: \( (5-3, 1-4, 6-1) = (2, -3, 5) \) Magnitude: \( \sqrt{2^2 + (-3)^2 + 5^2} = \sqrt{4+9+25} = \sqrt{38} \) Direction cosines: \( \left(\frac{2}{\sqrt{38}}, -\frac{3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\right) \)
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