Three Dimensional Geometry
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The shortest distance between lines $\vec{r} = \vec{a}_1 + \lambda \vec{b}$ and $\vec{r} = \vec{a}_2 + \mu \vec{b}$ (parallel lines) is:
(a) $\frac{|(\vec{a}_2 - \vec{a}_1) \times \vec{b}|}{|\vec{b}|}$
(b) $\frac{|(\vec{a}_2 - \vec{a}_1) \cdot \vec{b}|}{|\vec{b}|}$
(c) $|(\vec{a}_2 - \vec{a}_1) \times \vec{b}|$
(d) $0$
Step-by-Step Solution
Standard shortest distance formula for parallel lines. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\frac{|(\vec{a}_2 - \vec{a}_1) \times \vec{b}|}{|\vec{b}|}$: 1.0 Mark
Correct Answer: $\frac{|(\vec{a}_2 - \vec{a}_1) \times \vec{b}|}{|\vec{b}|}$
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