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Mathematics
Mathematics
Problem
a
⃗
=
i
^
−
2
j
^
+
3
k
^
\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}
a
=
i
^
−
2
j
^
+
3
k
^
,
b
⃗
=
2
i
^
+
j
^
−
k
^
\vec{b} = 2\hat{i} + \hat{j} - \hat{k}
b
=
2
i
^
+
j
^
−
k
^
,
c
⃗
=
λ
i
^
+
j
^
+
k
^
\vec{c} = \lambda\hat{i} + \hat{j} + \hat{k}
c
=
λ
i
^
+
j
^
+
k
^
and
v
⃗
=
a
⃗
×
b
⃗
\vec{v} = \vec{a} \times \vec{b}
v
=
a
×
b
. If
v
⃗
⋅
c
⃗
=
11
\vec{v} \cdot \vec{c} = 11
v
⋅
c
=
11
and the length of the projection of
b
⃗
\vec{b}
b
on
c
⃗
\vec{c}
c
is
P
P
P
, then
9
P
2
9P^2
9
P
2
is equal to
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