CUET · MATHS · PYQ PAPER 2023
The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:
- A \(\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3}\)
- B \(2 \hat{i}+\hat{j}+2 \hat{k}\)
- C \(\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{5}\)
- D \(\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{7}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 \hat{i}+\hat{j}+2 \hat{k}}{3}\)
Step-by-step Solution
Detailed explanation
\(\vec{R} = \vec{a} + \vec{b} = (2\hat{i} - \hat{j} + \hat{k}) + (2\hat{j} + \hat{k}) = 2\hat{i} + \hat{j} + 2\hat{k}\) \(|\vec{R}| = \sqrt{2^2 + 1^2 + 2^2} = \sqrt{4+1+4} = \sqrt{9} = 3\) \(\hat{R} = \frac{\vec{R}}{|\vec{R}|} = \frac{2\hat{i} + \hat{j} + 2\hat{k}}{3}\)
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