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 :
- A \(2 \hat{i}-\hat{j}-2 \hat{k}\)
- B \(9(2 \hat{i}-\hat{j}-2 \hat{k})\)
- C \(\frac{1}{9}(2 \hat{i}-\hat{j}-2 \hat{k})\)
- D \((6 \hat{i}-3 \hat{j}-6 \hat{k})\)
Answer & Solution
Correct Answer
(D) \((6 \hat{i}-3 \hat{j}-6 \hat{k})\)
Step-by-step Solution
Detailed explanation
\(|\vec{A}| = \sqrt{2^2 + (-1)^2 + (-2)^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\) \(\text{Unit vector } \hat{u} = \frac{2 \hat{i} - \hat{j} - 2 \hat{k}}{3}\) \(\text{Desired vector } \vec{V} = 9 \hat{u} = 9 \left( \frac{2 \hat{i} - \hat{j} - 2 \hat{k}}{3} \right)\)…
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