# The Lines 2x=3y=-z and 6x=-y=-4z

- are perpendicular
- are parallel
- intersect at an angle 45
^{o} - intersect at an angle 60
^{o}

**Answer: (1) Are Perpemdicular**

**Explanation:-
**2X = 3Y = -Z and 6X = – Y = – 4 Z

Here, a1 = 1/2, a2 = 1/6, b1 = 1/3, b2 = -1, c1 = -1 and c2 = -1/4

If a1.a2 + b1.b2 + c1.c2 = 0 ……………………. (1)

Then, the lines will be perpendicular.

Put the value of a1 = 1/2, a2 = 1/6, b1 = 1/3, b2 = -1, c1 = -1 and c2 = -1/4 in equation (1)

Then, 1 x 1/2 x 6 + 1 x (-1)/3 + (-1) x (-1)/4

= 1/12 – 1/3 + 1/4

= (1 – 4 + 3)/12

= (4 – 4)/12

= 0/12 = 0

Then, the lines are perpendicular.

Hence, the answer is (1) Are perpendicular.