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 θ/2,& along bisector

## Comments

Assignment Expert04.08.11, 20:16As 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)

tanmay04.08.11, 08:55can u please give me procedure?

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