Q:

the graph shows vectors a and b the resulting vector for b - a is blank, blank >, and the resulting vector for 2a -b is < blank, blank >.

Accepted Solution

A:
Answer:The resulting vector b - a is <-5 , 7> The resulting vector 2a - b is <8 , -9>Step-by-step 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>