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Mathematics
Mathematics
Problem
Let
a
\mathbf{a}
a
and
b
\mathbf{b}
b
be two non-collinear unit vectors. If
u
=
a
−
(
a
⋅
b
)
b
\mathbf{u} = \mathbf{a} - (\mathbf{a} \cdot \mathbf{b})\mathbf{b}
u
=
a
−
(
a
⋅
b
)
b
and
v
=
a
×
b
\mathbf{v} = \mathbf{a} \times \mathbf{b}
v
=
a
×
b
, then
∣
v
∣
|\mathbf{v}|
∣
v
∣
is a.
∣
u
∣
|\mathbf{u}|
∣
u
∣
b.
∣
u
∣
+
∣
u
⋅
a
∣
|\mathbf{u}| + |\mathbf{u} \cdot \mathbf{a}|
∣
u
∣
+
∣
u
⋅
a
∣
c.
∣
u
∣
+
∣
u
⋅
b
∣
|\mathbf{u}| + |\mathbf{u} \cdot \mathbf{b}|
∣
u
∣
+
∣
u
⋅
b
∣
d.
∣
u
∣
+
u
⋅
(
a
+
b
)
|\mathbf{u}| + \mathbf{u} \cdot (\mathbf{a} + \mathbf{b})
∣
u
∣
+
u
⋅
(
a
+
b
)
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