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CUET · MATHS · PYQ PAPER 2023

Choose the correct answer from the options given below:
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\) is \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{y-3}{-2}\)
B. Equation of line passing through (1, 2, 3) and parallel to the line given by \(\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}\) is \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z+3}{6}\).
C. Equation of line passing through the origin and (5, -2,3) is \(\frac{x}{5}=\frac{y}{-2}=\frac{z}{3}\).
D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is 2(x - 1) + 3(y - 2) - (z - 3) = 0.
E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is 2x + 3y + 4z = 1

  1. A A, E only
  2. B A, C, D only
  3. C C, D, E only
  4. D E only
Verified Solution

Answer & Solution

Correct Answer

(B) A, C, D only

Step-by-step Solution

Detailed explanation

A. Correct form: \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{z-3}{-2}\). Statement A is correct (assuming 'z' instead of 'y' in the last term). B. Given line direction ratios: \((3, -5, 6)\). Proposed line direction ratios: \((3, 5, 6)\). Not parallel. Statement B is incorrect. C. Line…