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# Vectors a, b and c are such that a+b+c=0 and |a| =3, |b|=5 and |c|=7 Find the angle between a and b - Mathematics

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#### Question

Vectors veca,vecb and vecc  are such that veca+vecb+vecc=0 and |veca| =3,|vecb|=5 and |vecc|=7  Find the angle between veca and vecb

#### Solution

We need to find the angle between veca and vecb

Now (veca+vecb+vecc)^2=(veca+vecb+vecc).(veca+vecb+vecc)

(veca+vecb+vecc)^2=(|veca|^2+|vecb|^2+|vecc|^2+2veca vecb+2vecc vecb+2veca vecc)

0=(9+25+49+2veca vecb+2vecc vecb+2veca vecc)

0=83+2(veca vecb+vecc vecb+veca vecc)

-83/2=(veca vecb+vecc vecb+veca vecc)

-83/2=(veca vecb+(-veca-vecb) vecb+(-veca-vecb) vecc) (because vecc=-veca-vecb)

-83/2=(-|vecb|^2-|veca|^2-vecavecb)

-83/2=(-|vecb|^2-|veca|^2-|veca||vecb|cos theta)

83/2=(34+15cosθ)

⇒83/2−34=15cosθ

⇒15/2=15cosθ

⇒1/2=cosθ

θ=π/3 or (5π)/3

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#### Video TutorialsVIEW ALL [2]

Vectors a, b and c are such that a+b+c=0 and |a| =3, |b|=5 and |c|=7 Find the angle between a and b Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors.
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