If k is any scalar and \vec{a}, \vec{b} be vectors then k \vec{a} + m\vec{a} can also be written as ________

(a) (k+m)\vec{a}

(b) \vec{a} + m\vec{a}

(c) k \vec{a} + \vec{a}

(d) mk\vec{a}

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This interesting question is from Multiplication of a Vector by a Scalar topic in section Vector Algebra of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

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Right answer is (a) (k+m)\vec{a}

The explanation: It satisfies distribution property over addition, hence in k \vec{a} + m\vec{a} we can take the vector \vec{a}

common and the answer come out to be (k+m)\vec{a}. Basically it’s a simplification method by which the vectors can be easily solved and further properties can be applied to them.