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If a and b are vectors such that \(\|{a}\| = 4\)\(\|{b}\| = 4\), and \(\|{a+b}\| = 7\), then find \(\|{2a-3b}\|\).

 Feb 2, 2019
 #1
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x=||2a-3b||

 

\(7^2=4^2+4^2- 2*4*4*cos(A) \\ \Rightarrow cos(A)=-\dfrac{17}{32} \)

\(x^2 =8^2+12^2-2*8*12*cos(180^{\circ}-A )\\ x^2=208+192*cos(A) \)

\(x = \sqrt{106 }\)

laugh

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 Feb 2, 2019

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