11. Let u. v, and w be three-dimensional real vectors. If u = , v =...

 

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11. Let u. v, and w be three-dimensional real vectors. If u =<-q, 10q, -q>, v = 3k + 10j + 7i, and w=< 2,2,2 >. Find (v)w पाली 12. Let u and v be three-dimensional real vectors. Suppose that u = √6i-88k and v=< 2,8, z>. Can u and v be parallel? If so find the values of z and y that make them parallel. If not show that it is impossible. 13. Find hrst when h(t, s, r) = e' sin(st) 14. Find the curvature of r(t) =< t², In(t), tln(t) > at the point (1,0,0) 15. Find and when yz +aln(y) = 2² 16. Verify that the function h(s, t) = sin(sat) satisfies the Wave Equation, h=²0¹ 17. Let u and v be three-dimensional real vectors. Suppose that u =< 1,1,1 > and v =< -3,66, -2>. Let r(t) = ²(u x v). Find the unit tangent vector T(t) at the point t = 1 18. Determine whether the following curves intersect for t, s € R. 5-12t, y = 3+9t, z = et C₁: C₂: x=3+8s, y = -6s, z = -(s²). 11. Let u. v, and w be three-dimensional real vectors. If u =<-q, 10q, -q>, v = 3k + 10j + 7i, and w=< 2,2,2 >. Find (v)w पाली 12. Let u and v be three-dimensional real vectors. Suppose that u = √6i-88k and v=< 2,8, z>. Can u and v be parallel? If so find the values of z and y that make them parallel. If not show that it is impossible. 13. Find hrst when h(t, s, r) = e' sin(st) 14. Find the curvature of r(t) =< t², In(t), tln(t) > at the point (1,0,0) 15. Find and when yz +aln(y) = 2² 16. Verify that the function h(s, t) = sin(sat) satisfies the Wave Equation, h=²0¹ 17. Let u and v be three-dimensional real vectors. Suppose that u =< 1,1,1 > and v =< -3,66, -2>. Let r(t) = ²(u x v). Find the unit tangent vector T(t) at the point t = 1 18. Determine whether the following curves intersect for t, s € R. 5-12t, y = 3+9t, z = et C₁: C₂: x=3+8s, y = -6s, z = -(s²).

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