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CUET · MATHS · PYQ PAPER 2025

The vector in the direction of the vector \(2 \hat{i}-\hat{j}-2 \hat{k}\) that has magnitude 9 units is :

  1. A \(2 \hat{i}-\hat{j}-2 \hat{k}\)
  2. B \(9(2 \hat{i}-\hat{j}-2 \hat{k})\)
  3. C \(\frac{1}{9}(2 \hat{i}-\hat{j}-2 \hat{k})\)
  4. D \((6 \hat{i}-3 \hat{j}-6 \hat{k})\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((6 \hat{i}-3 \hat{j}-6 \hat{k})\)

Step-by-step Solution

Detailed explanation

\(|\vec{A}| = \sqrt{2^2 + (-1)^2 + (-2)^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\) \(\text{Unit vector } \hat{u} = \frac{2 \hat{i} - \hat{j} - 2 \hat{k}}{3}\) \(\text{Desired vector } \vec{V} = 9 \hat{u} = 9 \left( \frac{2 \hat{i} - \hat{j} - 2 \hat{k}}{3} \right)\)…