Vectors: Vector equation of line MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Vector equation of lineHardQuestion 260015

Question

The vector equation of a line through point A (position vector a⃗) parallel to vector b⃗ is:

A
r⃗ = a⃗ + λb⃗
Correct
B
r⃗ = λa⃗ + b⃗
C
r⃗ = a⃗ × b⃗
D
r⃗ = a⃗ + b⃗

Correct answer

r⃗ = a⃗ + λb⃗

Explanation

Any point on the line through A parallel to b⃗ has position vector r⃗ = a⃗ + λb⃗ for some scalar λ ∈ ℝ. This is the parametric vector equation of the line.

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