Question

If vector a= (10,10) and vector b= (4,5)

then ||a+b|| ≠ ||a|| + ||b||. Explain.

I don't understand what this question is exactly asking, and I'm not sure how to answer it. Please explain. Thank you very much!!!

Answer 1

to explain, just evaluate:

|a| = √200
|b| = √41
a+b = (14,15)
|a+b| = √394 19.85
|a|+|b| = √200+√41 = 20.55

Seems clear to me.

if a and b are two sides of a parallelogram, a+b is the diagonal.

Clearly the indicated values cannot be equal unless a is parallel to b.