If a = i - j , b = i+j+k and c be a vector such that a x c + b = o and a. c= 4, then ici2 is equal to

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