Hi, I don't understand these questions and was unable to solve them. If you can please walk me through these questions and show work for all it would be really appreciated, thank you so much.

6. Find all points at which the curve with parametrization r(t) : (t 11 :2, t3 1) intersects the plane 1; = 1. Also nd the angle between the plane and the (tangent line to the) curve at each such point (in radians. to two decimal places). 7. The plane curve with parametrization r(t) = (6' cos 2t. e'sin 2:), t E R is an example of a Bernoulli spiral. (a) By hand or using MATLAB. sketch this curve. (b) Show that the angle a: between the position vector r(t} and the tangent vector r\" (t) is constant. Find the value of o in radians to two decimal places. 8. A particle's velocity is described by the function 5(3) = (o'- sin l, e", 6' cos it) for l E [0, 4]. (a) If the particle's initial position is {i, 1, i). describe its position and acceleration as functions of t. Hint: ge'ktint + cos ) = Ee'cost and lie'isint cos a\" = 28' sint. (b) Verify.' that the particle's path lies on a circular cone of the form 5:2 = Claim? + 2:2). and sketch the path. (c) What is the length of the particle's path from t = D to: = 4'? (d) Parameterize the particle's pooition in terms of arc length. (e) Compute the curvature of the space curve traced by the particle