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Mathematics
Problem
If
a
i
2
+
b
i
2
+
c
i
2
=
1
(
i
=
1
,
2
,
3
)
a_i^2 + b_i^2 + c_i^2 = 1 \,(i = 1, 2, 3)
a
i
2
+
b
i
2
+
c
i
2
=
1
(
i
=
1
,
2
,
3
)
and
a
i
a
j
+
b
i
b
j
+
c
i
c
j
=
0
(
i
≠
j
,
i
,
j
=
1
,
2
,
3
)
a_i a_j + b_i b_j + c_i c_j = 0 \,(i \neq j,\, i, j = 1, 2, 3)
a
i
a
j
+
b
i
b
j
+
c
i
c
j
=
0
(
i
=
j
,
i
,
j
=
1
,
2
,
3
)
then the value of
∣
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
∣
2
is
\begin{vmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{vmatrix}^2 \text{ is}
a
1
b
1
c
1
a
2
b
2
c
2
a
3
b
3
c
3
2
is
(a) 0 (b) 1/2 (c) 1 (d) 2 (a) 0 (b) 1/2 (c) 1 (d) 2
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