Two friends Raja and Rahul are standing on a point \( O \) from where they started to move in di...
0Two friends Raja and Rahul are standing on a point \( O \) from where they started to move in different directions with the position vector of \( 2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k} \) respectively. Raja reaches to his office at point \( A \) and Rahul reaches his client office at point \( B \) which are opposite to each other. They decided to meet at a coffee shop situated on the way of \( A B \) coffee shop divided the road \( A B \) in the ratio of \( 2: 1 \).
Give answers of the following questions : How much distance is covered by Raja to reach his office ' \( \mathbf{A}^{\prime} \) ?
(A) 6 units
(B) \( \sqrt{10} \) units
(C) \( \sqrt{6} \) units
(D) \( \sqrt{5} \) units
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