In unit-vector notation, what is the sum of vector a =(4m)i + (3m)j and vector b= (-13m)i +(7m)j?

Question

a)I got (27m)i +(10m)j but the book said it should have been (-9m)i +(10m)j

b)what is the magnitude and direction of vector a + vector b (relative to i)?

to find the magnitude i did the sqrt((-9^2 + 10^2) and then I got 13.453
I wasn't sure how to find the direction.

I am wondering how you got 27i? The i component of a was 4, and the i component of b was -13. Adding them gets the book answer.

Magnitude of the sum: (-13)^2 + (10)^2= 269, and the square of that is ....

Direction: arctan (10/-13)

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