Analytic Geometry Answers

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)

Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x² + y² + z² - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius

A cow is tied to one of the corners of the square field who side is 55 meters long.If the length of the rope is a tenth of the side field, what is the area of the field that is not grazed in cm2?

Calculate the equation for the plane containing the lines L1 and L2,where L1 is given by the parametric equation (x,y,z)=(1,0,-1)+t(1,1,1),t€R and L2 is given by the parametric equation (x,y,z)=(2,1,0)+t(1,-1,0),t€R.

Given that A = 2i + 3j - k, B = i - j +2k and C = 3i + 4j + k

a)find the unit vector along the direction of nA, for n<0

b) find the length of the projection of vector A on vector C

c)find the length of projection of vector C and vector A

d) find the sine of the angle between vector A and vector C