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Mathematics
Mathematics
Problem
The points
A
(
4
,
5
,
10
)
A(4, 5, 10)
A
(
4
,
5
,
10
)
,
B
(
2
,
3
,
4
)
B(2, 3, 4)
B
(
2
,
3
,
4
)
and
C
(
1
,
2
,
−
1
)
C(1, 2, -1)
C
(
1
,
2
,
−
1
)
are three vertices of a parallelogram
A
B
C
D
ABCD
A
B
C
D
, then a. Vector equation of
A
B
AB
A
B
is
2
i
+
3
j
+
4
k
+
λ
(
i
+
j
+
3
k
)
2\mathbf{i} + 3\mathbf{j} + 4\mathbf{k} + \lambda(\mathbf{i} + \mathbf{j} + 3\mathbf{k})
2
i
+
3
j
+
4
k
+
λ
(
i
+
j
+
3
k
)
b. Cartesian equation of
B
C
BC
B
C
is
x
−
2
1
=
y
−
3
1
=
z
−
4
5
\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{5}
1
x
−
2
=
1
y
−
3
=
5
z
−
4
c. Coordinates of
D
D
D
are
(
3
,
4
,
5
)
(3, 4, 5)
(
3
,
4
,
5
)
d.
A
B
C
D
ABCD
A
B
C
D
is a rectangle
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