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CUET · MATHS · PYQ PAPER 2023

Match List-I with List-II
List-IList-II
(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\)(I) \(\cos ^{-1}\left(\frac{2}{\sqrt{18}}\right)\)
(B) Angle between \(\hat{i}+\hat{j}+2 \hat{k}\) and \(2 \hat{i}+2 \hat{j}+4 \hat{k}\)(II) 0
(C) Angle between \(2 \hat{i}-\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)(III) \(90^{\circ}\)
(D) Angle between \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)(IV) \(\cos ^{-1}\left(\frac{1}{3}\right)\)

Choose the correct answer from the options given below:

  1. A (A)-(I),(B)-(II),(C)-(IV),(D)-(III)
  2. B (A)-(III),(B)-(II),(C)-(I),(D)-(IV)
  3. C (A)-(II),(B)-(III),(C)-(I),(D)-(IV)
  4. D (A)-(I),(B)-(IV),(C)-(III),(D)-(II)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\) \(\vec{a} = \hat{i}-2 \hat{j}+3 \hat{k}\), \(\vec{b} = 2 \hat{i}+\hat{j}\) \(\vec{a} \cdot \vec{b} = (1)(2) + (-2)(1) + (3)(0) = 2 - 2 + 0 = 0\) \(\cos \theta = 0\) \(\theta = 90^{\circ}\) Therefore, (A)…