Answer:
A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes, so \[\vec{a}+\vec{b},|\vec{a}+\vec{b}-\vec{c}|,\] angle between \[\vec{b}\] and \[\vec{c}\] and \[\lambda \vec{a}\]are independent of the orientation of the coordinate axes. But the quantity \[3{{a}_{x}}+2{{b}_{y}}\] depends upon the magnitude of the components along \[x\]- and y-axes, so it will change with the change in coordinate axes.
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