The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

Question

The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is (A) (π /3) (B) (π /4) (C) (π /2) (D) 0

Tardigrade Admin · Accepted Answer

Given, l+m+n=0 ...(i) and lm=0 i.e. either m=0 or l=0 If l=0 , then putting in equation (i), we get m=-n ∴ Direction ratios are 0,-n,n i.e. 0,-1,1 If m=0 , then putting in equation (i), we get l=-n ∴ Direction ratios are -n,0,n i.e. -1,0,1 ∴ cos θ =(0 × (- 1) + (- 1) × 0 + 1 × 1/√(0)2 + (- 1)2 + (1)2 √(- 1)2 + (0)2 + (1)2)=(1/2) ⇒ θ =(π /3)

Q. The direction cosines $l, m$ and $n$ of two lines are connected by the relations $l + m + n = 0$ and $l m = 0$ , then the angle between the lines is

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{2}$

$0$

Q. The direction cosines l,m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

3π​

4π​

2π​

0

Q. The direction cosines $l, m$ and $n$ of two lines are connected by the relations $l + m + n = 0$ and $l m = 0$ , then the angle between the lines is

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{2}$

$0$