Question

let a,b,c be vectors with magnitude 3,4,5 find a.b+ b.c+c.a if a+b+c=0​

Answer 1

Answer: -25

Step-by-step explanation:

Given: a = 3, b = 4, c = 5

           a+b+c=0

⇒a= -(b+c) and b = -(a+c) and c = -(a+b)

Now, we need to evaluate the expression

a·b + b·c + c·a = a·[-(a+c)] + b[-(b+c)] + c·[-(a+c)]

a·b + b·c + c·a = -a·a - a·c - b·b - b·c - c·a - c·c

2(a·b + b·c + c·a) = -(a·a + b·b + c·c)

2(a·b + b·c + c·a) = -(a² + b² + c²) [∵ x·x = x² ]

2(a·b + b·c + c·a) = -50

⇒a·b + b·c + c·a = -25