VEC014 · Vectors · Class 12 + B.Tech
Parallel vectors
Two vectors are parallel when one is a scalar multiple of the other; then their cross product is 0.
u ∥ vParallel vectors
📐 Formula
u ∥ v ⇔ v = ku ⇔ u₁v₂ − u₂v₁ = 0
✏️ Worked example
(2, 1) and (4, 2): (4, 2) = 2 × (2, 1), so they are parallel.
🌍 Where it is used
Checking that lines or forces act along the same direction.
❓ Quick check
Which is parallel to (3, −1)?
🏋️ Practice
EasyIs (1, 2) ∥ (−2, −4)?
Answer: Yes
MediumFind k: (2, k) ∥ (4, 6).
Answer: 3
ChallengeAre i and j parallel?
Answer: No