Scalar (dot) product
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Flip to reveal answersHow do you compute the scalar (dot) product of v and w?
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All 8 Flashcards — Scalar (dot) product
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Question
How do you compute the scalar (dot) product of v and w?
Answer
Multiply matching components and add: v·w = v₁w₁ + v₂w₂ + v₃w₃. The result is a single number.
Question
Is the dot product a vector or a number?
Answer
A number (scalar) — that's why it's called the scalar product.
Question
What is the formula linking the dot product to the angle?
Answer
v·w = |v||w| cos θ, so cos θ = (v·w)/(|v||w|).
Question
How do you find the angle between two vectors?
Answer
θ = cos⁻¹[ (v·w)/(|v||w|) ] — dot product over the product of the magnitudes.
Question
What does a NEGATIVE dot product tell you about the angle?
Answer
The angle is obtuse (between 90° and 180°), because cos θ is negative.
Question
How do you test if two vectors are perpendicular?
Answer
They are perpendicular exactly when v·w = 0.
Question
Find (1, 2, −2)·(3, 0, 1).
Answer
(1)(3) + (2)(0) + (−2)(1) = 3 + 0 − 2 = 1.
Question
To find a triangle's angle at vertex A, which vectors do you dot?
Answer
AB and AC (both pointing OUT from A); then cos A = (AB·AC)/(|AB||AC|).
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Full study notes for Scalar (dot) product
Topic 3.13 hub
Scalar & vector products (HL only)
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