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

Category: QuestionsIf k is any scalar and \(\vec{a}\), \(\vec{b}\) be vectors then k \(\vec{a}\) + m\(\vec{a}\) can also be written as ________
Editor">Editor Staff asked 11 months ago

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
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 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.