If a, b, c are non-collinear vectors such tha | vedclass

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(A) By definition,a set of vectors is linearly independent if the only linear combination that results in the zero vector is the one where all scalars

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$x = 0, y = 0, z = 0$

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(A) By definition,a set of vectors is linearly independent if the only linear combination that results in the zero vector is the one where all scalars are zero. Since $a, b, c$ are non-collinear vectors (and in the context of three-dimensional space,if they are linearly independent),the equation $xa + yb + zc = 0$ implies that $x = 0, y = 0, z = 0$. If at least one scalar were non-zero,the vectors would be linearly dependent,which contradicts the property of non-collinear vectors in this context.

If $a, b, c$ are non-collinear vectors such that for some scalars $x, y, z,$ $xa + yb + zc = 0,$ then

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