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Mathematics
Mathematics
Problem
For the vectors
a
,
b
,
c
\mathbf{a},\;\mathbf{b},\;\mathbf{c}
a
,
b
,
c
it is given that
∣
a
∣
=
3
,
∣
b
∣
=
2
,
∣
c
∣
=
4
,
|\mathbf{a}|=3,\quad |\mathbf{b}|=2,\quad |\mathbf{c}|=4,
∣
a
∣
=
3
,
∣
b
∣
=
2
,
∣
c
∣
=
4
,
a
⋅
b
=
2
,
a
⋅
c
=
−
1
,
b
⋅
c
=
3.
\mathbf{a}\cdot\mathbf{b}=2,\quad \mathbf{a}\cdot\mathbf{c}=-1,\quad \mathbf{b}\cdot\mathbf{c}=3.
a
⋅
b
=
2
,
a
⋅
c
=
−
1
,
b
⋅
c
=
3.
Calculate the value of
(
2
a
−
3
b
+
c
)
⋅
(
a
+
4
b
−
2
c
)
.
(2\mathbf{a}-3\mathbf{b}+\mathbf{c})\cdot(\mathbf{a}+4\mathbf{b}-2\mathbf{c}).
(
2
a
−
3
b
+
c
)
⋅
(
a
+
4
b
−
2
c
)
.
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