Question

three vectors a b c satisfy the condition a + b + c = 0 the quantity. u=a.b+b.c+c.a. if |a|=1|b|=4|c|=2​

Answer 1

Given,

a + b + c = 0

a + b = - c

Dot product with b on both sides

a.b + IbI^2 = - b.c

a.b + 16 = - b.c

a.b + b.c = - 16

again take dot product with c on both sides to

a + b = - c

so, a.c + b.c = - IcI^2

a.c + b.c = - 4

again dot product with a on both sides

IaI^2 + a.b = - a.c

a.b + a.c = -1

adding the three results

a.b + b.c + a.c + b.c + a.b + a.c = -16 -4 -1

2(a.b + b.c + c.a) = - 21

a.b + b.c + c.a = -21/2