Trigonometry- ??????

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!!!

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  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.

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