Analytic Geometry Answers

Convert the following rectangular coordinates into polar coordinates (r,θ) so that r < 0

and 0 ≤ θ ≤ 2π :

(4,−4√3)

. (a) Plot the following points in the same polar coordinates system

(3,π/4),(−3,π/4),(3,−π/4),(−3,−π/4)

(b) Convert into rectangular coordinates:

(4,−2π/3)

If a➡️ <a1,a2,a3>, b➡️ <b1,b2,b3> are two vectors in space

         Write down the formula of the cross product of these vectors and show all calculation.

Express the following surfaces in spherical coordinates (i) yz=2. (ii) y^2+z^2-x^2=1

Four forces act on an object such that the object is at rest. Three of the forces are given by

F1 = 2i −2j, F2 = i −4j, F4 = −3i −5j. Determine F3 and its magnitude

Find the centroid of the region.

The triangle with vertices (0, 0), (2, 0), and (0, 1).

By considering the angles between the vectors, show that a + b and a – b are

perpendicular when (a) = (b)

A plane with a velocity 400 km/h, 10 degrees, West of South encounters a wind with a

velocity of 40 km/h, from 35 degrees East of South. What is the plane’s resultant

velocity?

If (u) = 11, (v) = 23, and (u-v) = 30.

Find (u+v)