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  • If <img alt="(2x-3y+1)\vec{a}+\left ( 5x+7y-12 \right )\vec{b}=\vec{0}" src="https://learn.careers360.com/latex-image/?%282x-3y&plus;1%29%5Cvec%7Ba%7D&plus;%5Cleft%20%28%205x&plus;7y-12

If (2x-3y+1)\vec{a}+\left ( 5x+7y-12 \right )\vec{b}=\vec{0} where \vec{a}\, \, and\, \, \vec{b} are non-collinear then x+y equals

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

As we learned

Collinear Vectors -

x\hat{a}+y\hat{b}=\hat{0}\Rightarrow x= y= 0

- wherein

If and only if  \vec{a} and \vec{b} are non-collinear.

 

 \because a \, \, and\, \, b are non-collinear, so equation wil hold only when 2x-3y+1=0\, \, and 5x+7y-12=0

on solving, X=1, Y=1

\therefore x+y=2\, \, \, \, option (B)

 

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