Jignesh Patel
Assignment 4
MATH262, Fall 2010
due 10/13/2010 at 11:59pm EDT.
1.
(1 pt) Let
a
= (7, 6, 6) and
b
= (5, 5, 1) be vectors.
Compute the cross product
a
×
b
. (
,
,
)
2.
(16 pts) Consider the 3 points
P
= (
5
,

7
,
7
)
,
Q
=
(

2
,
8
,

8
)
and
R
= (
4
,

5
,

4
)
.
1. The equation of the plane passing through P,Q,R is
x
+
y
+
z
+
=
0
2. The parametric equations of the line L through P,Q are
x
=
+
t
y
=
+
t
z
=
+
t
3. The equation of the plane perpendicular to L and passing
through R is
x
+
y
+
z
+
=
0
3.
(1 pt) This question has two parts.
1. The point on the line
x
=
2

3
t
,
y
=

1

t
,
z
=

2
+
3
t
which is closest to the point (1,2,2) is
(
,
,
).
2. The point on the plane

3
x
+
3
y

3
z
=
2 that is closest
to the point (2,1,3) is
(
,
,
).
4.
(1 pt) Find points P,Q which are closest possible with P
lying on the line
x
=

1
+
2
t
,
y
=

1

2
t
,
z
=
3

6
t
and Q lying on the line
x
=

21
+
2
t
,
y
=
27
,
z
=
7

2
t
.
P = (