Which of the following statements about vector subtraction is correct?

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

Problem

Which of the following statements about vector subtraction is correct? (a) Vector subtraction is commutative, i.e. a−b=b−a\mathbf{a}-\mathbf{b}=\mathbf{b}-\mathbf{a} for all vectors. (b) Vector subtraction always yields a vector whose magnitude equals ∣∣a∣−∣b∣∣\bigl||\mathbf{a}|-|\mathbf{b}|\bigr|. (c) The associative relation (a−b)−c=a−(b−c)(\mathbf{a}-\mathbf{b})-\mathbf{c}=\mathbf{a}-(\mathbf{b}-\mathbf{c}) does not hold in general. (d) Vector subtraction preserves the magnitude of the original vectors.

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