If a and b are two non-collinear vectors and | vedclass

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(C) Given that $a$ and $b$ are two non-collinear vectors.We are given the equation $xa + yb = 0$.If $x 
eq 0$,then we can write $xa = -yb$,which impl

Vedclass · Accepted Answer

$x = 0$ and $y = 0$

Vedclass · Answer

(C) Given that $a$ and $b$ are two non-collinear vectors.We are given the equation $xa + yb = 0$.If $x 
eq 0$,then we can write $xa = -yb$,which implies $a = -(\frac{y}{x})b$.This means that vector $a$ is a scalar multiple of vector $b$,which implies that $a$ and $b$ are collinear.However,it is given that $a$ and $b$ are non-collinear,which is a contradiction.Therefore,our assumption that $x 
eq 0$ must be false,so $x = 0$.Substituting $x = 0$ into the equation $xa + yb = 0$,we get $0a + yb = 0$,which simplifies to $yb = 0$.Since $b$ is a non-zero vector,it follows that $y = 0$.Thus,for non-collinear vectors,$xa + yb = 0$ implies $x = 0$ and $y = 0$.

If $a$ and $b$ are two non-collinear vectors and $xa + yb = 0$,then:

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