Determine whether the statement is true or false. If it is true, explain/prove why. If it is false, give an example that disproves the statement. 1. For any vectors u and v in Ro, u . V = V . u. 8. For any vectors u, v, and w in R', ux (vxw) = (uxV Xw. 2. For any vectors u and v in R', ux v = v x u. 9. For any vectors u and v in R3, (ux v) . u = 0. 3. For any vectors u and v in R3, |Ju x vil = I/v x ull. 10. For any vectors u and v in R3, (utv) X v = ux v. 4. For any vectors u and v in R3 and any scalar k, k(u . v) = (ku) . v. 11. The cross product of two unit vectors is a unit vector. 5. For any vectors u and v in R3 and any scalar k, k(ux v) = (ku) x v. 12. The dot product of any two unit vectors is 1. 6. For any vectors u, v, and w in R3, (utv) xw = 13. The set of points {(x, y, z) | x2 + y2 = 1} is a uxw +v xw. circle. 7. For any vectors u, v, and w in R3, u . (vx w) = 14. If u = (u1, u2) and v = (v1, v2) then u . V = (uxv . W. (u102, U2V2)