Find a unit vector parallel to the vector 3 i +7 j +4 k . - Vidyadip

Question

Find a unit vector parallel to the vector $3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}.$

✓

Answer

Let $3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}=\vec{\text{a}}.$ $|\vec{\text{a}}|=\sqrt{3^2+7^2+4^2}$ $=\sqrt{9+49+16}=\sqrt{74}$ Using vector in the direction of $\vec{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}}{\sqrt{74}}$

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