Step by step
The question
Question: find 3u, when u = ⟨1, −2, 2⟩.
u = ⟨1, −2, 2⟩
1 Multiply by the numbers
3u means 3 times every part of u.
3u = ⟨3 × 1, 3 × (−2), 3 × 2⟩
3 times 1 is 3.
3 times (−2) is −6.
3 times 2 is 6.
3u = ⟨3, −6, 6⟩
So 3u = ⟨3, −6, 6⟩.
3u = ⟨3, −6, 6⟩
Careful!
The number multiplies every part, not only the first one.
Careful: not ⟨3, −2, 2⟩ ✗
2 Check
Let's check with a picture.
Here is u.
3u points the same way, 3 times as long.
Divide each part of the answer by 3.
We get back ⟨1, −2, 2⟩.
Right!
⟨3, −6, 6⟩ ÷ 3 = ⟨1, −2, 2⟩
Let's look back.
First: multiply by the numbers.
Last: check.
Answer
Careful: not ⟨3, −2, 2⟩ ✗