VEC013 · Vectors · Class 12 + B.Tech
Vector projection
The projection of u onto v is the 'shadow' of u along v.
projVector projection
📐 Formula
scalar projection = (u · v)/|v|; vector projection = ((u · v)/|v|²) v
✏️ Worked example
u = (3, 4) onto v = (5, 0): scalar 15/5 = 3, vector (3, 0).
🌍 Where it is used
Component of force along a ramp, shadows in graphics.
❓ Quick check
Projection of (2, 7) onto the x-axis?
🏋️ Practice
EasyScalar projection of (1, 1) on (1, 0)?
Answer: 1
MediumProjection of v on a perpendicular vector?
Answer: 0
ChallengeVector projection of (2, 2) on (0, 3)?
Answer: (0, 2)