Question

Determine the value of a+b if |3a| = 24 cm, |2b| = 10 cm and |3a-2b| = 20

Answer 1

I think something is wrong with your exercise, there is no a and b that match |3a| = 24 cm, |2b| = 10 that can get |3a-2b| = 20 .

Check image.
imgur(dot)com/08eylng(dot)jpg

Answer 2

This question was given to the class for a test and I have no idea how to do it.

We were given a similar question
imgur(dot)com/a/1P9wGFK

Answer 3

let's suppose a lies along the x-axis, and that 3a-2b makes an angle of θ with a. Then
|-2b|^2 = |3a|^2 + |3a-2b|^2 - 2*|3a|*|3a-2b|*cosθ
100 = 576+400-2*24*20cosθ
θ=24.15°
Then |-2b| makes an angle of 125.1° with |3a|
The components of -2b are thus (-5.75,8.18)
So, b=(2.87,-4.09) and a=(8,0)
and a+b = (10.87,-4.09)