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What is the component form of resultant of 4b −5a?

a  =   <1,-3>

b =    <-1,2>

 

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4b −5a= <___,___>

 May 6, 2020
 #1
avatar+24951 
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What is the component form of resultant of \(4\vec{b} -5\vec{a}\) ?

\(\vec{a} ~=~ <1,-3> \\ \vec{b} ~=~ <-1,2> \\ 4\vec{b} -5\vec{a} ~=~ < ~, ~> \)

 

\(\begin{array}{|rcll|} \hline \mathbf{4\vec{b} -5\vec{a}} &=& 4\dbinom{-1}{2} -5\dbinom{1}{-3} \\\\ &=& \dbinom{4(-1)-5(1)}{4\cdot 2-5(-3)} \\\\ &=& \dbinom{-4-5}{8+15} \\\\ &=& \dbinom{-9}{23} \\\\ \mathbf{4\vec{b} -5\vec{a}} &=& \mathbf{<-9,~23>} \\ \hline \end{array}\)

 

laugh

 May 6, 2020

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