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Problems
If
∣
a
a
2
1
+
a
3
b
b
2
1
+
b
3
c
c
2
1
+
c
3
∣
=
0
\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0
a
b
c
a
2
b
2
c
2
1
+
a
3
1
+
b
3
1
+
c
3
=
0
…
Mathematics
Problem
If
∣
a
a
2
1
+
a
3
b
b
2
1
+
b
3
c
c
2
1
+
c
3
∣
=
0
\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0
a
b
c
a
2
b
2
c
2
1
+
a
3
1
+
b
3
1
+
c
3
=
0
and vectors
(
1
,
a
,
a
2
)
(1, a, a^2)
(
1
,
a
,
a
2
)
,
(
1
,
b
,
b
2
)
(1, b, b^2)
(
1
,
b
,
b
2
)
and
(
1
,
c
,
c
2
)
(1, c, c^2)
(
1
,
c
,
c
2
)
are non-coplanar, then the product
a
b
c
abc
ab
c
equal to a. 2 b. -1 c. 1 d. 0
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