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Byju's Answer

Standard XII

Physics

Vector Addition

If the result...

Question

If the resultant of two vectors a and b and if the direction of reversed and the resultant is then which of the following is raise.

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Solution

$V e c t o r R = V e c t o r A + V e c t o r B$
$R = \sqrt{A^{2} + B^{2} + 2 A B c o s θ}$
$R^{2} = A^{2} + B^{2} + 2 A B c o s θ$
If the vector reversed that means direction will be reversed now the $c o s θ$ will be negative here
$S = v e c t o r A - v e c t o r B$
$S = \sqrt{A^{2} - B^{2} - 2 A B c o s θ}$
$S^{2} = A^{2} - B^{2} - 2 A B c o s θ$
Now $R^{2} + S^{2} = 2 (A^{2} + B^{2})$

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If the resultant of two vectors a and b and if the direction of reversed and the resultant is then which of the following is raise.

VectorR=VectorA+VectorBR=√A2+B2+2ABcosθR2=A2+B2+2ABcosθIf the vector reversed that means direction will be reversed now the cosθ will be negative hereS=vectorA–vectorBS=√A2−B2−2ABcosθS2=A2−B2−2ABcosθNow R2+S2=2(A2+B2)