When two vectors and add to give the zero vector

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

When two vectors A=(Ax,Ay)\mathbf{A}=(A_x, A_y) and B=(Bx,By)\mathbf{B}=(B_x, B_y) add to give the zero vector, which one of the following relations between their components is always true? (a) Ax=Bx and Ay=ByA_x=B_x \text{ and } A_y=B_y (b) Ax=−Bx and Ay=ByA_x=-B_x \text{ and } A_y=B_y (c) Ax=−Bx and Ay=−ByA_x=-B_x \text{ and } A_y=-B_y (d) Ax=By and Ay=−BxA_x=B_y \text{ and } A_y=-B_x

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