If \(\vec{A}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{B}=2\hat{i}-\hat{j}+4\hat{k}\) then the unit vector along \(\vec{A}+\vec{B}\) is
Answer & explanation
Correct answer: option 1
\(\begin{aligned}\vec{A}+\vec{B}=3\hat{i}+5\hat{k}&\\ \text{Thus, required vector }&=\frac{3\hat{i}+5\hat{k}}{|3\hat{i}+5\hat{k}|}=\frac{3\hat{i}+5\hat{k}}{\sqrt{34}}\end{aligned}\)