VEC015 · Vectors · Class 12 + B.Tech
Perpendicular vectors
Two non-zero vectors are perpendicular exactly when their dot product is 0.
u ⊥ vPerpendicular vectors
📐 Formula
u ⊥ v ⇔ u · v = 0
✏️ Worked example
(2, 1) · (−1, 2) = −2 + 2 = 0, so they are perpendicular.
🌍 Where it is used
Right angles in design and normal vectors.
❓ Quick check
Which is perpendicular to (1, 3)?
🏋️ Practice
EasyIs (4, 2) ⊥ (−1, 2)?
Answer: Yes
MediumFind k: (k, 2) ⊥ (3, −6).
Answer: 4
ChallengeIs i ⊥ j?
Answer: Yes