Question

The direction cosines of the perpendicular from the origin to the plane $3x-y+4z=5$ are

• A. $4,-1,3$
• B. $3,-1,4$
• C. $\frac{3}{\sqrt{26}},\frac{-1}{\sqrt{26}},\frac{4}{\sqrt{26}}$
• D. $\frac{4}{\sqrt{26}},\frac{-1}{\sqrt{26}},\frac{3}{\sqrt{26}}$

Answer 1

The correct option is C $\frac{3}{\sqrt{26}},\frac{-1}{\sqrt{26}},\frac{4}{\sqrt{26}}$

The direction ratios of the perpendicular from the origin to the plane $3x-y+4z=5$ are $(3,-1,4)$
Therefore, direction cosines are $(\frac{3}{\sqrt{3^2+1^2+4^2}},\frac{-1}{\sqrt{3^2+1^2+4^2}},\frac{4}{\sqrt{3^2+1^2+4^2}})=(\frac{3}{\sqrt{26}},\frac{-1}{\sqrt{26}},\frac{4}{\sqrt{26}})$
Ans: C