Given the vector u=<3,1,1>,v=<-2,0,4>.

A) compute the area of the parallelogram determined by u and v .
B) compute the vector. UxV

To compute the area of the parallelogram determined by vectors u and v:

A) We use the formula: Area = |u x v|

1. Compute the cross product of u and v:
1st component of the cross product = (1 * 4) - (1 * 0) = 4
2nd component of the cross product = (3 * 4) - (1 * -2) = 14
3rd component of the cross product = (3 * 0) - (1 * -2) = 2

2. Take the magnitude of the cross product:
|u x v| = √(4^2 + 14^2 + 2^2) = √(16 + 196 + 4) = √216 = 6√6

Therefore, the area of the parallelogram determined by u and v is 6√6.

To compute the vector U x V:

B) We use the cross product formula: U x V

1. Compute the cross product of u and v:
1st component of the cross product = (1 * 4) - (1 * 0) = 4
2nd component of the cross product = (3 * 4) - (1 * -2) = 14
3rd component of the cross product = (3 * 0) - (1 * -2) = 2

Therefore, the vector U x V = <4, 14, 2>.