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Mathematics
Mathematics
Problem
If
x
,
y
x, y
x
,
y
and
z
z
z
are distinct scalars such that
[
x
a
+
y
b
+
z
c
,
x
b
+
y
c
+
z
a
,
x
c
+
y
a
+
z
b
]
=
0
[x\mathbf{a} + y\mathbf{b} + z\mathbf{c}, x\mathbf{b} + y\mathbf{c} + z\mathbf{a}, x\mathbf{c} + y\mathbf{a} + z\mathbf{b}] = 0
[
x
a
+
y
b
+
z
c
,
x
b
+
y
c
+
z
a
,
x
c
+
y
a
+
z
b
]
=
0
where
a
,
b
\mathbf{a}, \mathbf{b}
a
,
b
and
c
\mathbf{c}
c
are non-coplanar vectors, then a.
x
+
y
+
z
=
0
x + y + z = 0
x
+
y
+
z
=
0
b.
x
y
+
y
z
+
z
x
=
0
xy + yz + zx = 0
x
y
+
y
z
+
z
x
=
0
c.
x
3
+
y
3
+
z
3
=
0
x^3 + y^3 + z^3 = 0
x
3
+
y
3
+
z
3
=
0
d.
x
2
+
y
2
+
z
2
=
0
x^2 + y^2 + z^2 = 0
x
2
+
y
2
+
z
2
=
0
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