Vector Algebra
Scalar Triple Product
Grade 12
Question:
<p>Given the direction vectors of two skew lines \(L_1\) and \(L_2\) as \(\hat{i}+\hat{j}\) and \(\hat{j}+\hat{k}\) respectively, the angle between them satisfies \(\cos\theta=\)</p>
<li>\(\dfrac{1}{\sqrt2}\)</li>
<li>\(\dfrac12\)</li>
<li>\(\dfrac{\sqrt3}{2}\)</li>
<li>\(0\)</li>
Step-by-Step Solution
Key Concept: cos \theta = |d_1 \cdot d_2|/(|d_1||d_2|). Compute dot product of (i+j) and (j+k).
$\vec{d_1}=\hat{i}+\hat{j},\;\vec{d_2}=\hat{j}+\hat{k}$.
$\cos\theta = \frac{|\vec{d_1}\cdot\vec{d_2}|}{|\vec{d_1}||\vec{d_2}|} = \frac{|0+1+0|}{\sqrt2\cdot\sqrt2}=\frac{1}{2}$
$\theta=60°$. Answer: (B)
Correct Answer: B