# A line passes through the point

Question:

A line passes through the point $\mathrm{A}(5,-2,4)$ and it is parallel to the vector $(2 \hat{\mathrm{j}}-\hat{\mathrm{j}}+3 \hat{\mathrm{K}})$. The vector equation of the line is

A. $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})$

B. $\overrightarrow{\mathrm{r}}=(5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})$

C. $\overrightarrow{\mathrm{r}} \cdot(5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})=\sqrt{14}$

D. none of these

Solution: