SATHEE: Straight Line Question 234

Straight Line Question 234

Question: The lines $ 2x=3y=-z $ and $ 6x=-y=-4z $

Options:

A) Are perpendicular

B) Are parallel

C) $ intersectatanangle45{}^\circ $

D) $ intersectatanangle60{}^\circ $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $ 2x=3y=-z $ or $ \frac{x}{3}=\frac{y}{2}=\frac{z}{-6} $ $ 6x=-y=-4z $ or $ \frac{x}{2}=\frac{y}{-12}=\frac{z}{-3} $ $ \cos \theta =\frac{x_1x_2+y_1y_2+z_1z_2}{\sqrt{x^2_1+x^2_2+x^2_3}.\sqrt{y^2_1+y^2_2+y^2_3}} $ $ =\frac{(6-24+18)}{\sqrt{{{(3)}^{2}}-{{(2)}^{2}}+{{(-6)}^{2}}}.\sqrt{2{{{{(}^{2}}+-12)}^{2}}+{{(-3)}^{2}}}} $ $ \cos \theta =0 $ $ \theta =90{}^\circ $ So lines are perpendicular

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Straight Line Question 234

Question: The lines $ 2x=3y=-z $ and $ 6x=-y=-4z $

Options:

Answer:

Solution:

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