A: With direction (3,2,−2) through (1,2,3): 3x−1=2y−2=−2z−3, correct in intent.
B: Direction ratios of given line are (3,−5,6); the option's denominators don't match - incorrect.
C: Direction (5,−2,3) through origin - correct.
D: Standard form of plane - correct.
E: Should be 2x+3y+4z=1, i.e. 6x+4y+3z=12, not 2x+3y+4z=1 - incorrect.
Correct: A, C, D.
Note: The last term in A reads 'y-3' in the original; we have read it as 'z-3' to match the intended line equation.
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector 3 i + 2 j - 2 k is x-1 3 = y-2 2 = y-3 -2. B. Equation of line…
CUET UG 2023 — Mathematics Geometry
2023mcqhard
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector 3i^+2j^−2k^ is 3x−1=2y−2=−2y−3.
B. Equation of line passing through (1, 2, 3) and parallel to the line given by 3x+3=54−y=6z+8 is 3x−1=5y−2=6z+3.
C. Equation of line passing through the origin and (5, -2, 3) is 5x=−2y=3z.
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)−1(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.
Choose the correct answer from the options given below:
Official previous-year question
Held on 25 May 2023 · Verified 13 Jul 2026.
Options
- A
A, E only
- B
A, C, D only
- C
C, D, E only
- D
E only
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