Problem 1.50

î

กำหนดให้ \(\vec{A} = 3.0\) และ \(\vec{B}\) ทำมุม \(θ\) กับ \(\vec{A}\)

îĵ

จะได้ \(\vec{B} = 4.0cosθ + 4.0sinθ\)

îĵ

\(\vec{A} + \vec{B} = (3.0 + 4.0\cos \theta ) + 4.0\sin \theta\)

\(|\vec{A} + \vec{B}|^{2} = (3.0 + 4.0\cos \theta )^{2} + (4.0\sin \theta )^{2}\)

\((6.0)^{2} = 9.0 + 24\cos \theta + 16\cos ^{2}\theta + 16\sin ^{2}\theta\)

\(36 = 9.0 + 24\cos \theta + 16\)

\(24\cos \theta = 11\cdots \cdots (1)\)

îĵ

\(\vec{A} - \vec{B} = (3.0 - 4.0\cos \theta ) - 4.0\sin \theta\)

\(|\vec{A} - \vec{B}|^{2} = (3.0 - 4.0\cos \theta )^{2} + (-4.0\sin \theta )^{2}\)

\(|\vec{A} - \vec{B}|^{2} = 9.0 - 24\cos \theta + 16\cos ^{2}\theta + 16\sin ^{2}\theta\)

\(|\vec{A} - \vec{B}|^{2} = 9.0 - 11 + 16; (1)\)

\(|\vec{A} - \vec{B}|^{2} = 14\)

\(|\vec{A} - \vec{B}| =\sqrt{14}\;\blacksquare\)