Question

Vector A = 3.00 + -1.00 and vector B = 3.00 + 4.00 . What is vector C = 2.00 A + 3.00 B?

Answer 1

Given:

$$\vec{A} = 3.00x + -1.00y,\\ \vec{B} = 3.00x + 4.00y.$$

What is

$$\vec{C}=2.00 \vec{A} + 3.00\vec{B}?$$

Just multiply both components of vector A by 2 and both components of vector B by 3:

$$2\vec{A} = 2\cdot3.00x + 2(-1.00)y=6x-2y,\\ 3\vec{B} = 3\cdot3.00x + 3\cdot4.00y=9x+12y.$$

Then add the corresponding components: x of A with x of B and y of A with y of B:

$$\vec{C}=6x-2y+9x+12y=15x+10y.$$