A problem I'm facing involves finding out the modulus of vectors. I understand that the modulus of a vector is the square of both the numbers and then the root of it to find the length. I was thinking for part (a) the answer would be 3 + (2*3) which is 9, and then the square root of this which will be 3. I used the same method to do part (b). However, I'm not sure whether what I have done is right, and I am stuck on part (c).
If $$b=2a$$ then we get $$|a+b|=|a+2a|=|3a|=3|a|$$
If $$b=-2a$$ then we get $$3|-a|=3|a|$$
If $a$ is perpendicular to $b$ then $$|a+b|^2=|a|^2+|b|^2=9+16=25$$ and $$|a+b|$$ gives $5$