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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 |
\(\frac{3\hat{i}+5\hat{k}}{\sqrt{34}}\) \(\frac{3\hat{i}+5\hat{k}}{\sqrt{24}}\) \(\frac{3\hat{i}-5\hat{k}}{\sqrt{34}}\) None |
\(\frac{3\hat{i}+5\hat{k}}{\sqrt{34}}\) |
| \(\begin{aligned}\vec{A}+\vec{B}=3\hat{i}+5\hat{k}&\\ \text{Thus, required vector }&=\frac{3\hat{i}+5\hat{k}}{|3\hat{i}+5\hat{k}|}=\frac{3\hat{i}+5\hat{k}}{\sqrt{34}}\end{aligned}\) |
