(a) Show that the set of all points in R2 lying on a line is a vector...

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(a) Show that the set of all points in R2 lying on a line is a vector space, with respect to the standard operations of vector addition and scalar multiplication, exactly when the line passes through the origin.
(b) Show that the set of all points in R3 lying on a plane is a vector space, with respect to the standard operations of vector addition and scalar multiplication, exactly when the plane passes through the origin.
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