Question

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A Very Good Afternoon....

Pleade help me with this....

When two vectors p and q act on an objects simultaneously , find expression for magnitude and direction of the result vector . For what angle of vectors , the resultant will have the same magnitude of these vectors when these vectors are equal to magnitude....

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Answer 1

Let each vector has a magnitude aawhich makes an angle θθ between them hence the resultant (RR) of these equal vectors
R=a2+a2+2a⋅acosθ−−−−−−−−−−−−−−−−√R=a2+a2+2a⋅acos⁡θ
=2a2+2a2cosθ−−−−−−−−−−−−√=2a2+2a2cos⁡θ
=a2–√1+cosθ−−−−−−−√=a21+cos⁡θ
=a2–√1+2cos2θ2−1−−−−−−−−−−−−√=a21+2cos2⁡θ2−1
=a2–√2cos2θ2−−−−−−√=a22cos2⁡θ2
=a2–√2–√cos