Dot product and the angle between two vectors
Compute the dot product of two vectors, and use it to identify perpendicular or parallel vectors. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Find the dot product u . v.
u = (−5, −1), v = (−3, −4)
Answer: 19
See one solved, step by step
Find the dot product u . v.
u = (−4, −3, 5), v = (−2, 5, 2)
📘 Worked solution
1u . v = (−4)(−2) + (−3)(5) + (5)(2)The dot product multiplies each pair of matching components.
2= 3Add the products together.
Ready to master it?
Jump into unlimited practice — your Winny Score tracks you to 100. And if it won't click, a real tutor will make it click: first lesson free.
Start practicing