The angle between the lines 2x = 3y = - z and 6x = - y = - 4z is

Question

The angle between the lines 2x = 3y = - z and 6x = - y = - 4z is (A) 0° (B) 45° (C) 90° (D) 30°

Tardigrade Admin · Accepted Answer

Given L1: 2x = 3y = - z and L2: 6x = - y = -4x ⇒ L1: (x/(1)2) = (y/(1)3) = (z/-1) and L2: (x/(1)16) = (y/-1) = (z/ - (1)4) Now, a1 a2 + b1 b2 + c1 c2 = ((1/2) ×(1/6)) + ((1/3) ×-1) + (-1 ×- (1/4)) = (1/12) - (1/3) + (1/4)= 0 ∴ Angle between L1 and L2 is 90°

Q. The angle between the lines $2 x = 3 y = - z$ and $6 x = - y = - 4 z$ is

$0^{\circ}$

$4 5^{\circ}$

$9 0^{\circ}$

$3 0^{\circ}$

Q. The angle between the lines 2x=3y=−z and 6x=−y=−4z is

0∘

45∘

90∘

30∘

Given L1​:2x=3y=−z and L2​:6x=−y=−4x ⇒L1​:21​x​=31​y​=−1z​ and L2​:161​x​=−1y​=−41​z​ Now, a1​a2​+b1​b2​+c1​c2​=(21​×61​)+(31​×−1)+(−1×−41​)=121​−31​+41​=0 ∴ Angle between L1​ and L2​ is 90∘

Q. The angle between the lines $2 x = 3 y = - z$ and $6 x = - y = - 4 z$ is

$0^{\circ}$

$4 5^{\circ}$

$9 0^{\circ}$

$3 0^{\circ}$