Determine the angle theta between the two cables Suppose tha

Determine the angle theta between the two cables. Suppose that a = 2 m and b = 4.4 m. Express your answer using three significant figures.

A = (2, -2, 3) m

B = (0, 2, 0 )

C = (-2, 2, 4.4) m

AC = C - A = -4i + 4j + 1.4 k

|AC| = sqrt(4^2 + 4^2 + 1.4^2) = sqrt(33.96)

AB = B - A = -2 i + 4j - 3 k

|AB| = sqrt(2^2 + 4^2 + 3^2) = sqrt(29)

Using dot product to find angle between AB and AC,

AB. AC = |AB||AC| cos@

(-2 i + 4j - 3 k ) . ( -4i + 4j + 1.4 k ) = sqrt(33.96) sqrt(29) cos@

cos@ = 0.631

@ = 51 deg