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

  1. are perpendicular
  2. are parallel
  3. intersect at an angle 45o
  4. intersect at an angle 60o
Anurag Mishra Professor Asked on 30th September 2015 in Maths.
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1 Answer(s)

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.

Anurag Mishra Professor Answered on 3rd October 2015.
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