Vector Algebra
Lines in Space
Grade 12
Question:
<p>Direction vectors of two lines \(L_1\) and \(L_2\) are \(\hat{i}-\hat{j}+\hat{k}\) and \(2\hat{i}+\hat{j}-\hat{k}\) respectively. The angle between the lines is</p>
<li>\(0\)</li>
<li>\(\dfrac{\pi}{6}\)</li>
<li>\(\dfrac{\pi}{2}\)</li>
<li>\(\dfrac{\pi}{3}\)</li>
Step-by-Step Solution
Key Concept: Compute d_1 \cdot d_2=(1)(2)+(-1)(1)+(1)(-1)=2-1-1=0. So cos \theta=0 \to \theta=\pi/2.
$\vec{d_1}\cdot\vec{d_2}=(1)(2)+(-1)(1)+(1)(-1)=2-1-1=0$.
The lines are perpendicular. $\theta=\dfrac{\pi}{2}$. Answer: (C)
Correct Answer: C