Three Dimensional Geometry
Oswaal
CBSE
Grade 12
Question:
Distance between parallel lines $\vec{r} = (\hat{i} + 2\hat{j} - 4\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})$ and $\vec{r} = (3\hat{i} + 3\hat{j} - 5\hat{k}) + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})$ is:
(a) $\frac{\sqrt{293}}{7}$
(b) $\frac{293}{7}$
(c) $\frac{\sqrt{293}}{49}$
(d) $7$
Step-by-Step Solution
Key Concept: d = |(a2-a1) x b| / |b| = |(2i+j-k) x (2i+3j+6k)| / 7 = \sqrt{9^2 + 14^2 + 4^2}/7 = \sqrt{293}/7.
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Correct Answer: $\frac{\sqrt{293}}{7}$
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