Page 218 -

Pb. 7.11 Find two unit vectors that are orthogonal to both vectors given by:
r r
− )
− , )2
a = (,21 and b = ( , ,1 23
Pb. 7.12 Find the area of the triangle with vertices at the points:

A( ,01− , ),1 B( , , ),3 1 0 and C( 2− ,,)0 2

Pb. 7.13 Find the volume of the parallelepiped formed by the three vectors:

r r r
u = ( , ,)12 0 , v = ( , ,),0 3 0 w = ( , , )12 3

Pb. 7.14 Determine the equation of a plane that passes through the point
(1, 1, 1) and is normal to the vector (2, 1, 2).
Pb. 7.15 Find the angle of intersection of the planes:

x +− = 0 and x − 3 y + − =1 0
y
z
z
Pb. 7.16 Find the distance between the point (3, 1, –2) and the plane z = 2x
– 3y.
Pb. 7.17 Find the equation of the line that contains the point (3, 2, 1) and is
perpendicular to the plane x + 2y – 2z = 2. Write the parametric equation for
this line.
Pb. 7.18 Find the point of intersection of the plane 2x – 3y + z = 6 and the line

x − 1 = y + 1 = z − 2
3 1 2
Pb. 7.19 Show that the points (1, 5), (3, 11), and (5, 17) are collinear.
r r r
Pb. 7.20 Show that the three vectors uv, ,and w are coplanar:
r r r
,
u = (, , );23 5 v = ( , , );2 8 1 w = ( ,8 22 12 )
Pb. 7.21 Find the unit vector normal to the plane determined by the points
(0, 0, 1), (0, 1, 0), and (1, 0, 0).

Homework Problem
Pb. 7.22 Determine the tetrahedron with the largest surface area whose ver-
2
2
2
tices P , P , P , and P are on the unit sphere x + y + z = 1.
0 1 2 3
© 2001 by CRC Press LLC