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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

What is the angle between the lines 2 x=3 y=-z and 6 x=-y=-4 z ?

What is the angle between the lines 2x=3y=−z2 x=3 y=-z and 6x=−y=−4z?6 x=-y=-4 z ?

Options

  1. A0∘0^{{}^{\circ}}
  2. B30∘30^{{}^{\circ}}
  3. C60∘60^{{}^{\circ}}
  4. D90∘90^{{}^{\circ}}

Correct answer

D. 90∘90^{{}^{\circ}}

Step-by-step solution

Given the lines 2x=3y=−z and 6x=−y=−4z⇒x3=y2=2−6 and x2=y−12=2−3\begin{aligned} & 2 x=3 y=-z \text{ and } 6 x=-y=-4 z \\ & \Rightarrow \frac{x}{3}=\frac{y}{2}=\frac{2}{-6} \text{ and } \frac{x}{2}=\frac{y}{-12}=\frac{2}{-3} \end{aligned} So, angle between lines is given by. cos⁡θ=∣3.2+2(−12)+(−6)⋅(−3)∣⇒cos⁡θ=0⇒θ=π2=90∘\begin{aligned} & \cos \theta=|3.2+2(-12)+(-6) \cdot(-3)| \\ & \Rightarrow \cos \theta=0 \Rightarrow \theta=\frac{\pi}{2}=90^{{}^{\circ}} \end{aligned}
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