Answered

IDNLearn.com is designed to help you find accurate answers with ease. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

Given three unit vectors a, b and c, such that a +b+c = 0, find a.b +b.c + c.a

Sagot :

Crisforpidn
a.(a +b + c ) = 0 => a.b + a.c = - a.a = - // a // ^2 = - 1 ( a is a unit vector )=> a.b + c.a =  - 1 ; 
where // // is Euclidean length;    ( * )

b.( a + b + c ) = 0 => b.a + b.c = - b.b => a.b + b.c = - // b // ^2 = -1 ( b is a unit vector );   ( * * )

c.( a + b + c ) = 0 => c.a + c.b = -c.c => a.c + b.c = - // c // ^ 2 = - 1 ; ( c is a unit vector )  ( * * * )

From ( * ), ( * * ), ( * * * ) => 2( a. b + b.c +  c.a ) = - 3 => a.b + b.c + c.a = - 3 / 2 = - 1.5
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.