Answer:
The resulting vector b - a is <-5 , 7>
The resulting vector 2a - b is <8 , -9>
Explanation:
* Use the graph to solve the problem
- The vector a is <3 , -2>
- The vector b is <-2 , 5>
* We can add and subtract the vectors
∵ a = <3 , -2>
∵ b = <-2 , 5>
- To find b - a subtract a from b
∴ b - a = <-2 , 5> - <3 , -2> = <(-2 - 3) , (5 - -2)> = <(-5) , (7)>
∴ The resulting vector b - a is <-5 , 7>
* 2a means multiply vector a by 2
∵ a = <3 , -2>
∴ 2a = <(2 × 3) , (2 × -2) = <6 , -4>
* Now lets find the resulting vector 2a - b
- Subtract b from 2a
∵ 2a = <6 , -4>
∵ b = <-2 , 5>
∴ 2a - b = <6 , -4> - <-2 , 5> = <(6 - -2) , (-4 - 5> = <(8) , (-9)> = <8 , -9>
∴ The resulting vector 2a - b is <8 , -9>