# 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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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

∴$$|\vec{a}+\vec{b}|=\sqrt{37}$$