Given the following vectors, calculate −7u+4v−7𝑢+4𝑣.u=⟨2,9⟩𝑢=⟨2,9⟩, v=⟨−8,0⟩
Question
Given the following vectors, calculate −7u+4v−7𝑢+4𝑣.u=⟨2,9⟩𝑢=⟨2,9⟩, v=⟨−8,0⟩
Solution
First, let's identify the vectors:
u = ⟨2,9⟩ v = ⟨−8,0⟩
The operation we need to perform is −7u + 4v.
Step 1: Multiply vector u by -7. This means multiplying each component of the vector by -7:
-7u = -7 * ⟨2,9⟩ = ⟨-14,-63⟩
Step 2: Multiply vector v by 4. This means multiplying each component of the vector by 4:
4v = 4 * ⟨-8,0⟩ = ⟨-32,0⟩
Step 3: Add the results from step 1 and step 2:
⟨-14,-63⟩ + ⟨-32,0⟩ = ⟨-14-32, -63+0⟩ = ⟨-46,-63⟩
So, −7u + 4v = ⟨-46,-63⟩.
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