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

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

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
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

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}.