Find \(|\vec{a}+\vec{b}|\), if \(|\vec{a}|=3 \,and \,|\vec{b}|=4 \,and \,\vec{a}.\vec{b}=6\).

Category: QuestionsFind \(|\vec{a}+\vec{b}|\), if \(|\vec{a}|=3 \,and \,|\vec{b}|=4 \,and \,\vec{a}.\vec{b}=6\).
Editor">Editor Staff asked 11 months ago

Find \(|\vec{a}+\vec{b}|\), if \(|\vec{a}|=3 \,and \,|\vec{b}|=4 \,and \,\vec{a}.\vec{b}=6\).
 
(a) 34
 
(b) \(\sqrt{37}\)
 
(c) 13
 
(d) \(\sqrt{23}\)
 
The question was asked in my homework.
 
This intriguing question originated from Product of Two Vectors-1 in chapter Vector Algebra of Mathematics – Class 12
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct answer is (b) \(\sqrt{37}\)
 
The explanation is: \(|\vec{a}+\vec{b}|^2=(\vec{a}+\vec{b}).(\vec{a}+\vec{b})\)
 
=\(\vec{a}.\vec{a}+\vec{a}.\vec{b}+\vec{b}.\vec{a}+\vec{b}.\vec{b}\)
 
=\(|\vec{a}|^2+2(\vec{a}.\vec{b})+|\vec{b}|^2\)
 
=(3)^2+2(6)+(4)^2
 
=9+12+16=37
 
∴\(|\vec{a}+\vec{b}|=\sqrt{37}\)