Question

If $l,m,n$ are the d.cs of the line joining $(5,-3,8)$ and $(6,-1,6)$ then $l+m+n=$

• A. $1$
• B. $\frac{1}{3}$
• C. $-1$
• D. $\frac{5}{3}$

Answer 1

Answer: (B)

$\frac{1}{3}$

The line joining $(5,-3,8)$ and $(6,-1,6)$ is given by the vector $-i+2j-2k.$

Hence, the direction cosines are given by:

$l=\frac{1}{\sqrt{1^2+2^2+(-2{)}^2}}=\frac{1}{3}$, $m=\frac{2}{\sqrt{1^2+2^2+(-2{)}^2}}=\frac{2}{3}$, $n=\frac{-2}{\sqrt{1^2+2^2+(-2{)}^2}}=\frac{-2}{3}$

$\Rightarrow l+m+n=\frac{1}{3}$