Question

The direction cosines of the line segment joining points $(-3,1,2)$ and $(1,4,-10)$ is.

• A. $\frac{4}{13},\frac{3}{13},-\frac{12}{13}$
• B. $\frac{-4}{13},\frac{3}{13},-\frac{12}{13}$
• C. $\frac{-4}{13},\frac{-3}{13},\frac{12}{13}$
• D. None of these

Answer 1

The correct option is A $\frac{4}{13},\frac{3}{13},-\frac{12}{13}$

The direction ratios of the line segment joining $A(-3,1,2)$ and $B(1,4,-10)$ are proportional to $1-(-3),4-1,-10-2,$ i.e., $4,3,-12$.
Now, its direction cosines are $\frac{4}{\sqrt{4^2+3^2+(-12{)}^2}},\frac{3}{\sqrt{4^2+3^2+(-12{)}^2}},\frac{-12}{\sqrt{4^2,3^2+(-12{)}^2}}$
or $\frac{4}{13},\frac{3}{13},-\frac{12}{13}$