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Question
The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is ______.
Options
0°
30°
45°
90°
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Solution
The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is 90°.
Explanation:
2x = 3y = – z
6x = – y = – 4z
`x/(1/2) = y/(1/3) = z/-1`
`x/(1/6) = y/-1 = z/((-1)/4)`
Direction cosine's of both lines are `(1/2, 1/3, -1)` and `(1/6, -1, -1/4)` respectively.
(l1, m1, n1) = (3, 2, – 6) and (l2, m2, n2) = (2, – 12, – 3)
cos θ = l1l2 + m1m2 + n1n2
= 6 – 24 + 18
= 0
`\implies` cos θ = 0 = cos 90°
∴ θ = 90°.
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