Problem 9. Determine whether the statement is true or false. If it is true, briefly explain why. If it is false, briefly explain why or give an example that disproves the statement. 1. For any vectors u and v, in R' (text uses V3), 10. For any vectors u and v in R3, u . V = V .u. (utv) x v = uxv. 2. For any vectors u and v, in R', uxv = vxu. 1 1. The cross product of two unit vectors is a unit 3. For any vectors u and v, in R', Juxv = vxull. vector. 4. For any vectors u and v, in R' and any scalar k, 12. A linear equation Ax + By + Cz = D represents a k(u . v) = (ku) . v . line in space. 5. For any vectors u and v, in R' and any scalar k, 13. The set of points { (x, y, z) | x + y =1, is a k(uxv) = (ku)xv. circle. 6. For any vectors u, v, and w in R3, 14. If u = (1,U2 ) and v = (v1, V2 ) , then (utv)xw =uxw+Vxw. u . V = (u V1 , UzV2 ) . 7. For any vectors u, v, and w in R3, u . (vxw) = (uxv) . w . 15. If u . v =0, then u =0 or v=0. 8. For any vectors u, v, and w in R3, 16. If uxv =0, then u =0 or v =0. ux(vxw) = (uxv) xw. 17. If u . v =0 and ux v =0, then u =0 or v =0. 9. For any vectors u and v, in R', (uxv) .u =0. 18. If u and v, in R3, u . v sullyl