Question
Write the direction cosines of the vector $\vec{\text{r}}=6\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$.
✓
Answer
Given: $\vec{\text{r}}=6\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$
Then, direction cosines of $\hat{\text{r}}$ are $\frac{6}{\sqrt{6^2+(-2)^2+3^2}},\frac{-2}{\sqrt{6^2+(-2)^2+3^2}},\frac{3}{\sqrt{6^2+(-2)^2+3^2}}$ or, $\frac{6}7,\frac{-2}7,\frac{3}7$
Then, direction cosines of $\hat{\text{r}}$ are $\frac{6}{\sqrt{6^2+(-2)^2+3^2}},\frac{-2}{\sqrt{6^2+(-2)^2+3^2}},\frac{3}{\sqrt{6^2+(-2)^2+3^2}}$ or, $\frac{6}7,\frac{-2}7,\frac{3}7$
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