Answer: IcI^2 = 9.5
Step-by-step explanation:
The data is:
a = (1, -1, 0)
b = (1, 1, 1)
axc = -b
then if c = (A, B, C) we have that:
axc = (-C, -C, A + B)
then we have the equality
-C = 1
A + B = 1
we also have that:
a.c = 1*A + (-1)*B + 0 *C = 4
A - B = 4
then we have two equations for A and B
A + B = 1
A - B = 4
we isolate A in the second equation and get:
A = 1 - B
now we replace it in the second equation
(1 - B) - B = 4
1 - 2B = 4
B =(4 -1)/(-2) = -3/2
then:
A + (-3/2) = 1
A = 1 + 3/2 = 2/2 + 3/2 = 5/2
we have that c = (5/2, -3/2, -1)
then IcI^2 = (5/2)^2 + (-3/2)^2 + (-1)^2 = 9.5
