Analytic Geometry Answers

If A,B,C,D,P,Q are six distinct collinear points ,show that

(AP.AQ)/(AB.AC.AD)+(BP.BQ)/(BC.BD.BA)+(CP.CQ)/(CD.CA.CB)+(DP.DQ)/(DA.DB.DC)=0

Let e = (1, 0) and f = (1, 1) be two points in 

R2 . Find ix - yl, 12x - y I , where x = e + f, 

y = 2e + 2f

The equation of the straight line is parallel to the straight line 2y=3x-1

Find the mass of the solid bounded by z = 1 and , 2 2 z = x + y the density function

being d (x, y, z) = | x | .

The line x-1/3=y+1/4=z-2/3 passes through the point (4,2,3).

A parallelepiped is defined by the following vectors |𝑎| = (2, 3, −1), |𝑏| = (−1, 0, 2),

and |𝑐| = (3, −1, 2). Find the volume of the parallelepiped. 

Find the cross product of (3, 2, 0) and (2, −1, −2), and use the dot product to confirm that your answer is correct. 

Two forces of magnitude 80𝑁 and 45𝑁 act on an object, with an angle between the forces of 100°. What is the resultant force?

 𝑊𝑋𝑌𝑍 is a parallelogram with 𝑊(0, −3), 𝑋(5, −1), and 𝑌(3, −4). Find the coordinates of point 𝑍. Recall that parallelogram points are listed in clockwise order.

Identify the center and the radius of the circle with the equation 〖2x〗^2+〖2y〗^2+10x=2y+7 in each item. Sketch its graph, and indicate the center.