Samadhi Gunasekera Senarath Dias Widhanaral
Assignment 4
MATH262, Fall 2008
due 10/25/2009 at 11:59pm EDT.
You may attempt each problem a maximum of 6 times.
1.
(1 pt) Let
a
= (2, 7, 5) and
b
= (9, 10, 3) be vectors.
Compute the cross product
a
×
b
. (
,
,
)
Correct Answers:
•
29
•
39
•
43
2.
(1 pt) Consider the 3 points
P
= (

1
,
1
,

2
)
,
Q
=
(

6
,
3
,
9
)
and
R
= (

1
,
3
,

3
)
.
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
Correct Answers:
•
24
•
5
•
10
•
39
•
1
•
5
•
1
•
2
•
2
•
11
•
5
•
2
•
11
•
22
3.
(1 pt) This question has two parts.
1. The point on the line
x
=
1
+
t
,
y
=
1
,
z
=

2
+
4
t
which
is closest to the point (1,2,1) is
(
,
,
).
2. The point on the plane

2
x

2
y
+
2
z
=

3 that is clos
est to the point (3,3,2) is
(
,
,
).
Correct Answers: