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# Vector Product - Dot product watch

1. Q)

Ans) I used the relationship:
A . B = |A| |B| cos x

so 30 = 5 |A| cos ab ---> 1
And 35= 5 |C| cos bc
now as |A| = |C|
it becomes: 35 = 5 |A| cos bc ----> 2

divide 1 by 2 to get: 30/35 = cos ab /cos bc
now here is how i imagined those angles to be:

I then used the trigonometric identities to get:
6/7 [cos(theta) cos 35 + sin (theta) sin 35] =cos (theta) cos60 + sin (theta) sin 60
I then rearranged it to get tan and then inverse it and got theta = 61.6 degrees and the answer is 28.4 degrees.

Where did i go wrong? Any help please will be utterly appreciated
Thanks a lot
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2. I would start by multiplying the two dot product equations to give A · B · B · C = 30 x 35, which simplifies to
A · C = 1050 / |B|. since you know the angle ac you can work out the modulus of A, which you can then use in the A · B relationship to find a value for angle ab.

Obviosluy this gives you two possible values for theta, so be careful which one you take as the answer

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