Question

The distance of the point $B(i+2j+3k)$ from the line which is passing through $A(4i+2j+2k)$ and which is parallel to the vector $c=2i+3j+6k,$ is

• A. $10$
• B. $\sqrt{10}$
• C. $2\sqrt{10}$
• D. none of these

Answer 1

Answer: (B)

$\sqrt{10}$

$A=4i+2j+2k$

$B=i+2j+3k$

$C=2i+3j+6k$

${BM}^2={AB}^2-{AM}^2$ ....(1)

$AB=(-3,0,1)=-3i+0j+k{AB}^2=9+1=10$

$AM+$ Projection of $AB$ in the direction of

$C=2i+3j+6k$

$AM=\frac{AB.C}{\left|C\right|}=\frac{(-3i+0j+k)(2i+3j+6k)}{7}=0$

$\therefore$ From equation (1) we have

${BM}^2=10-0=10\Rightarrow BM=\sqrt{10}$