Question

If k is any scalar and \(\vec{a}\), \(\vec{b}\) be vectors then k (\(\vec{a}\)+ \(\vec{b}\))= ________

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

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

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

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

I had been asked this question by my college director while I was bunking the class.

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

Answer 1

Correct answer is (a) k\(\vec{a}\) + k\(\vec{b}\)

The explanation is: Multiplication of vector by scalar satisfies distributive property over addition and in k (\(\vec{a}\)+ \(\vec{b}\)) we multiply k with \(\vec{a}\), \(\vec{b}\) individually and hence the answer comes out to be k\(\vec{a}\) + k\(\vec{b}\).