Analytic Geometry Answers

Plot the following points in the polar coordinates system (3,π\4),(-3,π\4),(3,-π\4),(-3,-π\4)

Convert into rectangular coordinates (4,-2π\3)

Show that the centre of all sections of the sphere x² + y ² +z² = r² by the planes through a point (a,b,c) lie on the sphere x(x-a)+y(y-b)+z(z-c)=0

Find the centres of the spheres. which touch at the the plane 4x+3y=47 at the point (8,5,4) and which touch the Sphere x² + y ² +z² = 1

Convert the following rectangular coordinates into polar coordinates (r , theta) so that r<0 and 0<theta <2pi: ( 4, -4 square root of 3)

Prove that |a+b| - |a-b| ≤ 2|b|.

Given z1=2<45degrees, z2=3<120degrees, z3=4<180degrees. Determine the following:

a) (z1)^2+z2/z2+z3

b) z1/z2*z3

Convert (3–√,−1) into polar coordinates (r,θ) so that r≥0 and 0≤θ<2π.

Write z1=3–√+i and z2=1−i in trigonometric form. Then the argument of the quotient z1z2is given by

Given r1 = 3i − 4j + 3k, r2 = 5i + 3j − 6k, r3 = 2i + 7j + 3k and r4 = 4i + 3j + 5k.

Find the scalars a, b and c such that r4 = ar1 + br2 + cr3