Analytic Geometry Answers

Given triangle ABC has vertices at (-2,4),(-2,-4) and (0,-2), respectively, find the circumcenter of the triangle.

Part 1: Centres of a Triangle
Consider the triangle , where . In this part of the assignment, you will use proper mathematical notation and organization to find the following. Remember to show your work and use the rubric to ensure that you have addressed all parts of the evaluation.
 Find the coordinates of the centroid (one type of "centre of a triangle")
 Find the coordinates of the orthocentre (a second type of "centre of a triangle")  Find the coordinates of the circumcentre (a third type of "centre of a triangle")  State any relationship you see between the three key points you found above.

A small television has a picture with a diagonal measure of 10 inches and a viewing area of 48 square inches. Find the width and length of the screen.

Prove that If the tangent vector of the parameterized curve is constant, the image of the curve is (part of) a straight line.

Q. What are the projections of helix (acost, asint, t) in all three coordinate planes xy-plane, yz-plane, xz-plane.

The direction of a vector V(Xv,Yv,Zv) intersects a sphere on point “B”. Assuming O(0,0,0) as the centre and ‘r’ as the radius of the sphere. The mirror of the vector based on OB direction passes the point C(0,0,h). The “B” coordination, B(Xb,Yb,Zb), is required based on the above parameters.

Find the area of an equilateral triangle inscribed in the circle x2+y2 - 6x + 2y – 15 = 0.

Find the magnitude of vector a=3i-2j+2k

Find a unit vector parallel to the resultant vector A1=2i+4j−5k, A2=1+2j+3k
a) 3/7i+6/7j−2/7k
b)1/7i+63/7j−4/7
c)2/7i−3/7j−5/7
d)3/5i+6/5j−2/5