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CUET · MATHS · PYQ PAPER 2023

Match List - I With List - II
List - IList - II
(A) The area of parallelogram determined by vectors \(2 \hat{i}\) and \(3 \hat{j}\)(I) 2
(B) The value of \((\hat{i} \times \hat{j}) \cdot \hat{k}+(\hat{j} \times \hat{k}) \cdot \hat{i}\)(II) 4
(C) The value of a for which the vectors \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(a \hat{i}-6 \hat{j}+8 \hat{k}\) are collinear.(III) 0
D. The value of \(\lambda\) for which the vectors \(2 \hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are perpendicular.(IV) 6
Choose the correct answer from the options given below.

  1. A А - І, В - ІI, С - III, D - IV
  2. B А-II, В - І, С - III, D - IV
  3. C А - III, В - IV, C - II, D - I
  4. D A - IV, B - I, C - II, D - III
Verified Solution

Answer & Solution

Correct Answer

(D) A - IV, B - I, C - II, D - III

Step-by-step Solution

Detailed explanation

A. \( |(2 \hat{i}) \times (3 \hat{j})| = |6 \hat{k}| = 6 \) A - IV B. \( (\hat{i} \times \hat{j}) \cdot \hat{k} + (\hat{j} \times \hat{k}) \cdot \hat{i} = \hat{k} \cdot \hat{k} + \hat{i} \cdot \hat{i} = 1 + 1 = 2 \) B - I C.…