Question

If a+b+c=0 and a =12 b =5 c =13 find the angle between a and b

Answer 1

Answer

90 degree

Explanation

Given,

m(A) = 12, m(B) = 5, m(C) = 13, where m(X) stands for magnitude of X.

A + B = C

squaring both sides,

A.A+ B.B + 2 A.B = C.C

note 'dot’ product i.e. A.A is equal to m(A)ˆ2.

=> m(A)ˆ2 + m(B)ˆ2 + 2 m(A)m(B)cos(ab) = m(C)ˆ2 , where ab is the angle between A and B.

Substituting the values in the above equation,

=> 144 + 25 +120cos(ab) = 169

=> 169 + 120cos(ab) = 169

=> 120cos(ab) = 0

=> cos(ab) = 0

=> cos(ab) = cos(pi/2) or cos(90deg)

ab = pi/2 or 90deg, where ab is the angle between A and B.