Question

If a b c are vectors such that a+b+c=0 and a=7 b=5 c=3 then the angle between vector b and c is

Answer 1

Let angle between vector A and B is X. Also magnitude of A is equal to magnitude of B.
Therefore
|A+B|=n|A−B|Squaring both side we have|A|2+2A.B+|B|2=n2(|A|2−2A.B+|B|2)Using |A|=|B| in above equation we have2(n2−1)|A|2=2(1+n2)A.B(n2−1)|A|2=(1+n2)A.B(n2−1)|A|2=(1+n2)|A||B|CosXAgain using |A|=|B| in above equation we haveCosX=(n2−1)(1+n2)X=Cos−1[(n2−1)(1+n2)]

Answer 2

Answer:

Answer is 60 degrees.

Step-by-step explanation:

Given,

a + b + c = 0,

Transpose "a" to other side of equation.

⇒ b + c = -a

(Square on both sides)

⇒  \ b | ² + | c | ² + 2 |b| |c| cosβ = | a |²

(Substitute the values given, we get...)

⇒ 5² + 3² +  2 X 5 X 3 cosβ = 7²

⇒25 + 9 + 30 cosβ = 49

⇒ cosβ = (49 - 34) / 30

⇒cos β = 1/2 = cos (π/3) or cos 60°

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