MATH 1300 D01/D02 Winter 2016 Assignment 2
SHOW ALL WORK to get full marks. Leave answers as exact answers. For example,
leave it as fractions such as 1
{
7 as opposed to decimals such as 0
.
142857
.
Word problems
should have sentence answers with units. Fractions should be lowest terms.
1.
[5]
Determine an equation of the plane through the points
P
p
1
,
´
1
,
3
q
, Q
p
2
,
´
1
,
0
q
and
R
p
3
,
1
,
´
2
q
.
Your answer should be in standard form.
2.
[5]
Determine an equation of the line through the points
P
p
1
,
´
3
,
2
q
and
Q
p
6
,
2
,
´
1
q
in:
(a) parametric form.
(b) symmetric form.
3. For the lines
x
“
5
t, y
“
2
´
3
t, z
“
3
´
2
t
and
2
x
´
3
10
“
y
´
1
´
3
“
4
´
z
2
:
(a)
[2]
Show that the lines are parallel.
(b)
[5]
Calculate the distance between the parallel lines.
4. For the lines
x
1
“ p
1
,
2
,
´
3
q `
s
p
1
,
´
2
,
0
q
and
x
2
“ p
1
,
´
3
,
1
q `
t
p
1
,
5
,
3
q
:
(a)
[5]
Show that the lines are skew.
(b)
[4]
Calculate the cosine of the angle between the skew lines.
(c)
[5]
Calculate the distance between the skew lines.
5.
(a)
[6]
Determine the two planes parallel to the plane 2