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

Category: QuestionsIf \(\vec{a}\) =\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\) and λ=5, what is value of λ\(\vec{a}\)?
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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\(\hat{k}\).