Question

the resultant vector P and Q is R.on reversing the direction of the angle the resultant becomes S.show that R sq.+S sq.=2(P sq.+Q sq.)

Answer 1

Magnitude of Resultant R be R1
P1=Magnitude of Vector P
Q1=Magnitude of vector Q
Then,
R1=squareroot of(P1 sq +Q1 sq)
Therefore R1 sq.=(P1 sq.+Q1 sq)
Now, The direction is changed so resultant S is formed
Let S1 be the magnitude of resultant vector S.
Then,
S1=squareroot of(P1 sq +Q1 sq)
Therefore S1 sq.=(P1 sq.+Q1 sq)
As here in the question direction is not calculated so..
On adding
R1 sq.+S1 sq.=R sq.+S sq. Also,
P1=P
Q1=Q
Therefore,
R sq.+ S sq.=(P sq.+Q sq.) + (P sq.+ Q sq.)
==>R sq. + S sq.=2(P sq.+Q sq)
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