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Vector equation of a line passing through point with position vector a and parallel to vector b is
Ar = a × b
Br = a + b
Cr = a + t b
Dr = a · b t
Answer & Solution
Correct answer: C. r = a + t b
1. A line passing through A (position vector a) and parallel to b consists of all points whose position vector has the form a + t b.
2. Here t is a real parameter.
3. Hence r = a + t b.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 6 "Line and Plane" §6.2_
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