Question

The projection of the join of the points $(3,4,2),(5,1,8)$ on the line whose d.c's are $\left(\frac{2}{7},\frac{3}{7},\frac{6}{7}\right)$ is

• A. $7$
• B. $\frac{31}{7}$
• C. $\frac{42}{13}$
• D. $\frac{38}{13}$

Answer 1

Answer: (B)

$\frac{31}{7}$

Let $A\equiv (3,4,2);B\equiv (5,1,8)$

$\overline{AB}=2\hat{i}-3\hat{j}+6\hat{k}$

$\overline{a}=dc=\frac{2}{7}\hat{i}+\frac{3}{7}\hat{j}+\frac{6}{7}\hat{k}$

$Projection=\overline{AB}\times \overline{a}=\frac{4}{7}-\frac{9}{7}+\frac{36}{7}=\frac{31}{7}$