Question

If \(\vec{a}\) =\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\) and λ=5, what is value of λ\(\vec{a}\)?

(a) \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

(b) 5\(\hat{i}\) + 5\(\hat{j}\) + 5\(\hat{k}\)

(c) \(\hat{i}\) + 5\(\hat{j}\) + 5\(\hat{k}\)

(d) 10\(\hat{i}\) + 10\(\hat{j}\) + 10\(\hat{k}\)

This question was addressed to me at a job interview.

My doubt stems from Multiplication of a Vector by a Scalar in division Vector Algebra of Mathematics – Class 12

Answer 1

Right option is (b) 5\(\hat{i}\) + 5\(\hat{j}\) + 5\(\hat{k}\)

To explain I would say: Multiplication of vector \(\vec{a}\) =\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\) by scalar value 5 results in 5\(\hat{i}\) + 5\(\hat{j}\) + 5\(\hat{k}\), as in these type of questions we multiply\(\hat{i}\), \(\hat{j,}\)

\(\hat{k}\) with the constant given and the answer comes out to be 5\(\hat{i}\) + 5\(\hat{j}\) + 5\(\hat{k}\).