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Mathematics
Mathematics
Problem
Find all values of
λ
\lambda
λ
such that
x
,
y
,
z
≠
(
0
,
0
,
0
)
x, y, z \neq (0, 0, 0)
x
,
y
,
z
=
(
0
,
0
,
0
)
and
(
i
^
+
j
^
+
3
k
^
)
x
+
(
3
i
^
−
3
j
^
+
k
^
)
y
+
(
−
4
i
^
+
5
j
^
)
z
=
λ
(
x
i
^
+
y
j
^
+
z
k
^
)
(\hat{i} + \hat{j} + 3\hat{k})x + (3\hat{i} - 3\hat{j} + \hat{k})y + (-4\hat{i} + 5\hat{j})z = \lambda(x\hat{i} + y\hat{j} + z\hat{k})
(
i
^
+
j
^
+
3
k
^
)
x
+
(
3
i
^
−
3
j
^
+
k
^
)
y
+
(
−
4
i
^
+
5
j
^
)
z
=
λ
(
x
i
^
+
y
j
^
+
z
k
^
)
, where
i
^
,
j
^
\hat{i}, \hat{j}
i
^
,
j
^
and
k
^
\hat{k}
k
^
are unit vectors along the coordinate axes.
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