Step by step
The question
Question: find the dot product of u = ⟨6, 0, −2⟩ and v = ⟨1, 7, 3⟩.
⟨6, 0, −2⟩ • ⟨1, 7, 3⟩
1 Multiply the matching parts
The dot product: multiply the matching parts: x times x, y times y, z times z.
Then add.
u • v = 6 × 1 + 0 × 7 + −2 × 3
6 times 1 is 6.
0 times 7 is 0.
−2 times 3 is −6.
u • v = 6 + 0 − 6
Add them up: u • v = 0.
u • v = 0
Careful!
The dot product is not a vector.
We add the three products.
The answer is one number.
Careful: not ⟨6, 0, −6⟩ ✗
2 Check
Let's check: the other order, v dot u.
We get 0 again.
Right!
v • u = 1 × 6 + 7 × 0 + 3 × (−2) = 0
A dot product of 0 means a square corner: the vectors are perpendicular.
0 → exactly 90°
Let's look back.
First: multiply the matching parts.
Last: check.
Answer
Careful: not ⟨6, 0, −6⟩ ✗