Dot product & angle between vectors
Practice Flashcards
Flip to reveal answersDot product of v = (v₁,v₂,v₃) and w = (w₁,w₂,w₃) in components?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Dot product & angle between vectors
Sign up free to track progress and get spaced-repetition review schedules.
Question
Dot product of v = (v₁,v₂,v₃) and w = (w₁,w₂,w₃) in components?
Answer
v·w = v₁w₁ + v₂w₂ + v₃w₃ — multiply matching components and add. The answer is a number.
Question
Geometric formula for the dot product?
Answer
v·w = |v||w|cos θ, where θ is the angle between the vectors.
Question
How do you find the angle between two vectors?
Answer
cos θ = (v·w)/(|v||w|), then θ = cos⁻¹ of that value.
Question
Is the dot product a vector or a number?
Answer
A number (a scalar) — that's why it's called the SCALAR product.
Question
Magnitude of a vector (v₁,v₂,v₃)?
Answer
|v| = √(v₁² + v₂² + v₃²) — the length of the arrow.
Question
a = (2,−1,3), b = (4,0,−2): find a·b.
Answer
(2)(4)+(−1)(0)+(3)(−2) = 8 + 0 − 6 = 2.
Question
If the dot product of two vectors is 0, what is the angle?
Answer
90° — they are perpendicular.
Question
u = (1,2,2), v = (2,0,−1): find the angle between them.
Answer
u·v = 0, so cos θ = 0 and θ = 90°.
Read the notes
Full study notes for Dot product & angle between vectors
Topic 3.13 hub
Scalar product (HL only)
More from Topic 3.13
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free