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) 30° (B) 45° (C) 90° (D) 0°

Tardigrade Admin · Accepted Answer

The given equations can be rewritten as (x/3)=(y/2)=(z/-6) and (x/2)=(y/-12)=(z/-3) ∴ Angle between the lines is given by cos θ=(6-24+18/√9+4+36√4+144+9) =(0/√49√157)=0 ⇒ θ=90°

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

$3 0^{\circ}$

$4 5^{\circ}$

$9 0^{\circ}$

$0^{\circ}$

The given equations can be rewritten as
$\frac{x}{3} = \frac{y}{2} = \frac{z}{- 6}$ and $\frac{x}{2} = \frac{y}{- 12} = \frac{z}{- 3}$
$∴$ Angle between the lines is given by
$cos θ = \frac{6 - 24 + 18}{9 + 4 + 36 4 + 144 + 9}$
$= \frac{0}{49 157} = 0$
$\Rightarrow θ = 9 0^{\circ}$

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

30∘

45∘

90∘

0∘