The acute angle between two lines such that the direction cosines l,m,n, of each of them satisfy the equations l+m+n=0 and l2+m2-n2=0 is:

Question

The acute angle between two lines such that the direction cosines l,m,n, of each of them satisfy the equations l+m+n=0 and l2+m2-n2=0 is: (A) 15°  (B) 30°  (C) 60°  (D) 45°

Tardigrade Admin · Accepted Answer

Let l1,m1,n1 and l2,m2,n2 be the d.c of line 1 and 2 respectively and angle between lines, θ is cosθ =l1l2+m1m2+n1n2 Now, as given l2+m2=n2 and l+m=-n ⇒ (-n )2-2lm=n2⇒ 2lm=0 or lm=0 So the direction ratios of the two lines will be (0 , 1 , 1) &(1 , 0 , 1) ∴ cosθ =(1/2)⇒ θ =60° (acute angle)

Q. The acute angle between two lines such that the direction cosines $l, m, n,$ of each of them satisfy the equations $l + m + n = 0$ and $l^{2} + m^{2} - n^{2} = 0$ is:

$1 5^{\circ}$

$3 0^{\circ}$

$6 0^{\circ}$

$4 5^{\circ}$

Q. The acute angle between two lines such that the direction cosines l,m,n, of each of them satisfy the equations l+m+n=0 and l2+m2−n2=0 is:

15∘

30∘

60∘

45∘

Q. The acute angle between two lines such that the direction cosines $l, m, n,$ of each of them satisfy the equations $l + m + n = 0$ and $l^{2} + m^{2} - n^{2} = 0$ is:

$1 5^{\circ}$

$3 0^{\circ}$

$6 0^{\circ}$

$4 5^{\circ}$