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

JEE Main · 2005 · 08 May 2005 · Offline · Three Dimensional Geometry

The angle between the lines

2 x = 3 y = - z

and

6 x = - y = - 4 z

(A) $0^{0}$
(B) $9 0^{\circ}$ ✓ Correct
(C) $4 5^{\circ}$
(D) $3 0^{\circ}$

Answer: (B)

Solution

Rewriting

2 x = 3 y = - z

\frac{x}{3} = \frac{y}{2} = \frac{z}{- 6}

gives direction ratios

(3, 2, - 6)

, and

6 x = - y = - 4 z

\frac{x}{2} = \frac{y}{- 12} = \frac{z}{- 3}

gives

(2, - 12, - 3)

. Their dot product is

3 (2) + 2 (- 12) + (- 6) (- 3) = 6 - 24 + 18 = 0

, so the lines are perpendicular and the angle between them is

9 0^{\circ}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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