I do not understand anything about vector multiplication. I have to do questions

Question

I do not understand anything about vector multiplication. I have to do questions 7 and 9 for the 8th edition of Fundamentals of Physics by Halliday and Resnick and the expert answer does not help me at all. Can somebody please explain this to me?
Thanks.
I do not understand anything about vector multiplication. I have to do questions 7 and 9 for the 8th edition of Fundamentals of Physics by Halliday and Resnick and the expert answer does not help me at all. Can somebody please explain this to me?
Thanks.

Explanation / Answer

7)Let the height of the room be , h = (3m) j Length of the room be , l = (3.70 m) i a)The magnitude of displacement is    D = v(3)^2+(3.70)^2       = 4.76 m b)No the length of the path is not less than this path d)Equal, since length of the path is v(3)^2+(3.70)^2 = 4.76 m e) In unit vector notation      D = 4.76 m cos? i + 4.76 m sin? j f) The length of the shortest path is 3.70 m-3.0 m = 0.70 m --------------------------------------------------------------------------------- 9)Given vector a = (4.0 m)i+(3.0m)j             b = (-13.0 m)i+(7.0 m)j a +b = (4.0 -13.0) i + (3.0 +7.0 )j        = -9.0 i+10.0 j b) magnitude of a+b = v(-9.0)^2+(10.0)^2                               = 13.45 m c)direction ? = tan^-1(10.0/-9.0)                     = 138^0

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