Answer to Question #3815 in Trigonometry for tanmay

Question #3815
Two vectors having equal magnitudes A make an angle θ with each other.The magnitude and direction of resultant are respectively: <br>a) 2Acos θ/2, along bisector <br>b) Acos θ/2, at 45 degree from one vector <br>c) Acos θ/2, along bisector <br>d)Asin θ/2, along bisector
Expert's answer
a) 2A cos &theta;/2,& along bisector

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Assignment Expert
04.08.11, 20:16

As you can see on the image,
two equal vectors AB and AC form the isosceles triangle ABC,
the resultant is the diagonal of the rhomb ABDC,
BC is the other diagonal.
In the rhomb the diagonals intersect in the middle and at right angle. Thus AO is the height and the middle line of the triangle ABC.
As ABC is isosceles triangle, AO is also the bisector of the angle BAC. So the angle BAO is θ/2.
AO = AB* cos (BAO) = a cos ( θ/2)
AD = 2 AO = 2a cos ( θ/2)

04.08.11, 08:55

can u please give me procedure?

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