Analytic Geometry Answers

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, -2>, v = <8, 24> 

ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC. 

a and b denote the vectors OA and OB, indicate on the same diagram the vectors OCand ODdenoted by a+b and a−b. Draw on another diagram the vector OE denoted by a+2b

ABCD is a square and P,Q are the midpoint of BC,CD respectively. If AP=a and AQ=b,find in terms of a and b,the directed line segments of AB,AD,BD and AC

Suspension bridge are known to be normal around the world especially in developed countries. These bridges usually have towers of some sort and cables, both of which have great importance in the integral stability of the bridge. A STEM student makes some plans for his project on a suspension bridge . He first tries to draw his model.The two towers are 12 meters high and 20 meters apart (10 meters away each from the origin in the center), and the cable he drew between and from the top of the two towers are of course, parabolic. The lowest point of tge cable is 3 meters above the origin. He shows this model to his teacher, and the teacher asks him" what is the vertical distance from the road to the cable at 5 metersaway from the center?" What is the answer toTeacher's question?

The vertices of a triangle are F (-3, 6), G (1, -6) and H (5, 2). For line segment FG, there is a midpoint P and Q is the midpoint of FH. a) Show that PQ is parallel to GH b) PQ is half the length of GH

ansform the equation 17𝑥

2 + 18𝑥𝑦 − 7𝑦

2 − 16𝑥 − 32𝑦 − 18 = 0 to one in 

which there is no term involving 𝑥, 𝑦.