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Consider a line = ( i + 4 j) + λ(2 i - 2 j + 3 k), then which of the following statements are correct? (A) it passes through point (9, -4, 12) (B) it…

CUET UG 2025 — Mathematics Geometry

2025mcqmedium

Consider a line r⃗=(i^+4j^)+λ(2i^−2j^+3k^)\vec{r} = (\hat{i} + 4\hat{j}) + \lambda(2\hat{i} - 2\hat{j} + 3\hat{k})r=(i^+4j^​)+λ(2i^−2j^​+3k^), then which of the following statements are correct?

(A) it passes through point (9, -4, 12)

(B) it passes through point (1, 4, -1)

(C) its direction cosine's are 217,−217,317\frac{2}{\sqrt{17}}, \frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}17​2​,17​−2​,17​3​

(D) its Cartesian equation is x−12=y−4−2=z3\frac{x - 1}{2} = \frac{y - 4}{-2} = \frac{z}{3}2x−1​=−2y−4​=3z​

Choose the correct answer from the options given below:

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A), (C) and (D) only

  2. B

    (B) and (C) only

  3. C

    (A) and (C) only

  4. D

    (B) and (D) only

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