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Mathematics
Mathematics
Problem
If
a
^
,
b
^
\hat{a}, \hat{b}
a
^
,
b
^
and
c
^
\hat{c}
c
^
are the three unit vectors and
α
,
β
\alpha, \beta
α
,
β
and
γ
\gamma
γ
are scalars such that
c
^
=
α
a
^
+
β
b
^
+
γ
(
a
^
×
b
^
)
\hat{c} = \alpha\hat{a} + \beta\hat{b} + \gamma(\hat{a} \times \hat{b})
c
^
=
α
a
^
+
β
b
^
+
γ
(
a
^
×
b
^
)
. If it is given that
a
^
⋅
b
^
=
0
\hat{a} \cdot \hat{b} = 0
a
^
⋅
b
^
=
0
and
c
^
\hat{c}
c
^
makes equal angle with both
a
^
\hat{a}
a
^
and
b
^
\hat{b}
b
^
, then evaluate
α
2
+
β
2
+
γ
2
\alpha^2 + \beta^2 + \gamma^2
α
2
+
β
2
+
γ
2
.
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