Answer:
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
