(Solved): Math 163use the knowlege from12.1:3D coordinate systems12.2: Vector12.3:the Dot product12.4:the Cros ...

(b) Find an equation of a plane through the point $$(0,1)$$ that makes the angle $$?$$ with the $$xy$$-plane. Assume $$0<?<?/2$$. (c) Use trigonometric functions to parameterize the curve of intersection of the cone and the plane. Hint: Start by parameterizing the cone as $$(x,y,z)=(r\cos ?,r\sin ?,kr),r?\mathbb{R},??[0,2?),$$ where the choice of the constant $$k$$ depends on your choice of the cone in part (a). (d) Choose two values for $$?$$ to get two curves of intersection, one bounded the other unbounded. Then parameterize a specific tangent line to each of these curves. (e) Graph the cone, the curves of intersection, and the tangent lines in GeoGebra. (f) (Optional) Define $$?$$ as a slider by using the Slider command in GeoGebra. Show and describe how the curve of intersection varies with $$?$$. As always, be sure to explain your thinking in a way that would help a struggling classmate. Part II: Help a Classmate. (a) Write an equation of a right circula with its.vertex at the origin and symmetric about the $$z$$-axis. Note that has two "halves". 1 (b) Find an equation of a plane through the point $$(0,1)$$ that makes the angle $$?$$ with the $$xy$$-plane. Assume $$0<?<?/2$$.