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Mathematics
Mathematics
Problem
If
a
=
x
i
^
+
(
x
−
1
)
j
^
+
k
^
\mathbf{a} = x\hat{i} + (x-1)\hat{j} + \hat{k}
a
=
x
i
^
+
(
x
−
1
)
j
^
+
k
^
and
b
=
(
x
+
1
)
i
^
+
j
^
+
a
k
^
\mathbf{b} = (x+1)\hat{i} + \hat{j} + a\hat{k}
b
=
(
x
+
1
)
i
^
+
j
^
+
a
k
^
make an acute angle,
∀
x
∈
R
\forall x \in \mathbb{R}
∀
x
∈
R
, then find the values of
a
a
a
.
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