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Arrange the magnitude of vectors subtraction $(\bar{A} - \bar{B})$ so that their magnitudes are in decreasing order. If the two vectors $\bar{A} and \bar{B}$ are acting at an angle $(| \vec{A} | > | \vec{B} |)$
$A) 60^{0}$ $B) 90^{0}$ $C) 180^{\circ}$ $D) 120^{\circ}$

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C, D, B, A

C, D, A, B

A, B, D, C

D, C, B, A

answer is C.

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Detailed Solution

$R^{2} = A^{2} + B^{2} + 2 ABcos (180 - θ)$

$R^{2} = A^{2} + B^{2} - 2 ABcos θ$

$if θ = 60^{\circ}; R^{2} = A^{2} + B^{2} - AB$

$if θ = 90^{\circ}; R^{2} = A^{2} + B^{2}$

$if θ = 180^{\circ}; R^{2} = A^{2} + B^{2} + 2 AB$

$if θ = 120^{\circ}; R^{2} = A^{2} + B^{2} + AB$

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