Analytic Geometry Answers

If \\(a=3i-2j+k\\), \\(b=2i-4j-3k\\) and \\(c=-i+2j+2k\\), find the magnitude of \\(a+b+c\\)

Answer the questions and show complete solutions.

6. A plane through the origin is perpendicular to the plane 2

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

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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