1. Find the tangent vector r(t) at the point where t=3 given r(t)=(4cos(t))i+(3sin(t))j+(3t)k a) r(3)=3j+3k b) r(3)=3j+9k c) r(3)=4i3j+9k d) r(3)=4i3j+3k e) r(3)=3j+9k 2. Give the vector parameterization of the tangent line to r(t)=(e^3t)i+ (e^3t)j+(3ln(t))k at the point where t=1 a) R(u)=(e^3i+e^3j+k)+u(3e^3i3e^3j+3k) b) R(u)=(e^3i+e^3j+3k)+u(3e^3i+3e^3j+k) c) R(u)=(e^3i+e^3j)+u(3e^3i+3e^3j+k) d) R(u)=(e^3i+e^3j+3k)+u(3e^3i3e^3j+3k) e) R(u)=(e^3i+e^3j)+u(3e^3i3e^3j+3k) 3. Give the vector parameterization of the tangent line to r(t)=(3^t2)i+(1t)j+(2^t2+1)k at the point P(3,0,3) a) R(u)=(3i+3k)+u(i+2j+k) b) R(u)=(3i+3k)+u(9i+5k) c) R(u)=(3i+3k)+u(6ij+4k) d) R(u)=(3i+3k)+u(7i2j+12k) e) R(u)=(3i+3k)+u(i+2j+3k) 4. Scalar parametric equations for the line tangent to the graph of r(t)=(1+3t)i+ (t^2+3t+2)j+(t^3+4t1)k at the point P(1,2,1) are: a) x(t)=3+t,y(t)=3+2t,z(t)=4t b) x(t)=1+3t,y(t)=2+3t,z(t)=1+4t c) x(t)=1+2t,y(t)=2+6t,z(t)=1+3t d) x(t)=3+t,y(t)=5+2t,z(t)=7t e) x(t)=1+3t,y(t)=2+5t,z(t)=1+7t 5. Find the points on the curve r(t)=(4t)i+(t^2+1)j at which r(t) and r(t) are perpendicular. a) (4,1) b) (0,1) c) (1,0) d) (2,5) e) (3,0) 6. Find the points on the curve r(t)=(3t)i+(t^2+1)j at which r(t) and r(t) have the same direction. a) (3,2) b) (3,2) c) (1,2) d) (4,0) e) (2,4) 7. Find the points on the curve r(t)=(4t)i+(t^2+4)j at which r(t) and r(t) have opposite direction. a) (3,3) b) (2,8) c) (8,8) d) (8,4) e) (5,3) 8. Find the point at which the curves r1(t)=(e^2t)i+(4sin(t+/2))j+(t^23)k and r2(u)=(u)i+(4)j+(u^24)k intersect and find the angle of intersection. a) (1,4,3) ,=arccos(2/5) b) (1,4,3),=arccos(1/3) c) (1,4,3) ,=arccos(1/5) d) (1,4,3),=arccos(2/5) e) (0,4,3),=arccos(2/3) 9. and 10. picture \f\f\f