Question

The direction cosines of the line joining the points $(2,3,-1)$ and $(3,-2,1)$ are

• A. $-1,5,-2$
• B. $\frac{1}{\sqrt{30}}$,$-\sqrt{\frac{5}{6}}$,$\sqrt{\frac{2}{15}}$
• C. $\frac{-1}{30}$,$\frac{1}{6}$,$-\frac{1}{15}$
• D. none of these

Answer 1

Answer: (B)

$\frac{1}{\sqrt{30}}$,$-\sqrt{\frac{5}{6}}$,$\sqrt{\frac{2}{15}}$

Step 1:

The direction ratios of the line joining these points are

$x_2-x_1,y_2-y_1,z_2-z_1$

$(i.e)(3-2),(-2-3),(1-(-1\left)\right)$

$⟹$ we get $(1,-5,2)$

Step 2:

Its direction cosines are :$\frac{1}{\sqrt{30}},-\sqrt{\frac{5}{6}},\sqrt{\frac{2}{15}}$