Finda + b, 8a + 9b, |a|, and |a − b|.(Simplify your answer completely.)a =leftangle0.gif−3, 4rightangle0.gifb =leftangle0.gif9, −1rightangle0.gifa + b = 8a + 9b = |a| = |a − b| =

Step-by-step explanation:

Given the following vectors a = (-3,4) and b = (9, -1)

|a| and |b| are the modulus of a and b respectively.

|a| = √(-3)²+4²

|a| = √9+16

|a| = √25

|a| = 5

Similarly;

|b| = √(9)²+1²

|b| = √81+1

|b| = √82

We are to find the following;

a) a + b

a+b =  (-3,4)  +  (9, -1)

a+b = (-3+9, 4+(-1))

a+b = (6, 4-1)

a+b = (6,3)

b) 8a + 9b

8a + 9b = 8(-3,4)  + 9(9, -1)

8a + 9b = (-24,32)  + (81, -9)

8a + 9b = (-24+81, 32+(-9))

8a + 9b = (57, 32-9)

8a + 9b = (57, 23)

c) |a| = √(-3)²+4²

|a| = √9+16

|a| = √25

|a| = 5

d)  |a − b|

To get  |a − b|, we need to get a-b first

Solve for a -b

a-b =  (-3,4)  -  (9, -1)

a-b = (-3-9, 4-(-1))

a-b = (-12, 4+1)

a-b = (-12,5)

Find modulus of a-b i.e   |a − b|,

|a − b| = √(-12)²+5²

|a − b| = √144+25

|a − b| =√169

|a − b| = 13