Answer:
(A⃗ ×B⃗ )⋅C⃗ = - 76.415
Step-by-step explanation:
First we need to calculate (A⃗ ×B⃗ ) :
(A⃗ ×B⃗ ) = A.B.sin (α).n
Where A is the magnitude of A⃗
Where B is the magnitude of B⃗
Where α is the angle between A⃗ and B⃗ = 63.9 - 25.6 = 38.3
Finally n is the vector orthogonal to A⃗ and B⃗
n magnitude is 1 and his direction is given by the right hand-rule
so n = ( 0 , 0 , 1 )
(A⃗ ×B⃗ ) = A.B.sin (α).n = 5.08 . 3.94 . sin (38.3) . (0 , 0 , 1 ) = (0,0,12.4)
C⃗ can be written as C.(0,0,-1) because of his +z - direction
C.(0,0,-1) = 6.16.(0,0,-1) = (0,0,-6.16)
(A⃗ ×B⃗ )⋅C⃗ = (0,0,12.4).(0,0,-6.16) = -76.41480787 = -76.415
