Question

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\(\vec{a}\)

I got this question during an interview for a job.

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

Answer 1

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.