Analytic Geometry Answers

Answer the two questions and show the complete solutions.


4.Show that the line x/3 = y/-2 = z/2 is parallel to the plane 2

Answer the two questions and show complete solution.


2. Find two unit vectors that are parallel to the

Show correct and complete solution.


1. Find the volume of the parallelepiped with the vertices in the given order: (0, 0, 0), (3, 0, 0), (0, 5, 1), (2, 0 , 5), (3, 5, 1), (5, 0, 5), (2, 5, 6), and (5, 5, 6). Sketch the solid.

Which of the following statements is/are true? Explain why the false one is false.

A. If u = (u1; u2) with ui 6= 0 for some 1  i  2; then the unit vector in the direction of u is

p 1

u21

+u22

(u1; u2) : (2)

B. u = (1; 2; 3) is the unit vector in the direction of u: (

Consider the vectors :


u = (1,0) and v= (0,1)


1) Determine CosA, where A is the angle between u and v.


2) Determine the area of the parallelogram determined by u and v.

b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)



i) )8,6,6(

ii) ( 1,1,2 )

Suppose u, v and w are vectors in 3-space,where u =(u1u2, u3), v =(v1, v2, v3) and w= (w1, w2, w3).


Express ( u * v) * w as a determinant.

Find the value of mif it is given that the line y=mxis 4 units from the point (4,-1)

Find the equation of the ciFind the equation of the tangent with the slope 3/4


to the circle x^2+y^2=13

which is tangent to the x at (6,0) and tangent to the y-axis

Show that the closed sphere with centre (2,3,7)and radius 10 in R^3 is contained in the open cube P = {(x, y,z): |x − 2 |<11, |y − 3| <11, |z − 7| <11}.

Show that the closed sphere with centre (2,3,7) 3and radius 10 in 3 R is contained in the

open cube P = {(x, y,z :) x − 2 <11, y − 3 <11, z − 7 <11}.