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CUET · MATHS · PYQ PAPER 2025

A vector of magnitude 8 units in the direction perpendicular to both the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{k}\) is

  1. A \(8(\hat{i}+\hat{j}-2 \hat{k})\)
  2. B \(\frac{8}{\sqrt{6}}(-\hat{i}+\hat{j}+2 \hat{k})\)
  3. C \(\frac{8}{\sqrt{6}}(\hat{i}+\hat{j}-2 \hat{k})\)
  4. D \(\frac{8}{\sqrt{6}}(\hat{i}-\hat{j}+2 \hat{k})\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{8}{\sqrt{6}}(\hat{i}+\hat{j}-2 \hat{k})\)

Step-by-step Solution

Detailed explanation

\( \vec{A} = \hat{i}+\hat{j}+\hat{k} \) \( \vec{B} = 2\hat{i}+\hat{k} \) \( \vec{C} = \vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 0 & 1 \end{vmatrix} = \hat{i}(1-0) - \hat{j}(1-2) + \hat{k}(0-2) = \hat{i}+\hat{j}-2\hat{k} \)…