Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
p
⃗
=
2
i
^
+
j
^
+
3
k
^
\vec{p} = 2\hat{i} + \hat{j} + 3\hat{k}
p
=
2
i
^
+
j
^
+
3
k
^
and
q
⃗
=
i
^
−
j
^
+
k
^
\vec{q} = \hat{i} - \hat{j} + \hat{k}
q
=
i
^
−
j
^
+
k
^
. If for some real numbers
α
\alpha
α
,
β
\beta
β
, and
γ
\gamma
γ
, we have
15
i
^
+
10
j
^
+
6
k
^
=
α
(
2
p
⃗
+
q
⃗
)
+
β
(
p
⃗
−
2
q
⃗
)
+
γ
(
p
⃗
×
q
⃗
)
,
15\hat{i} + 10\hat{j} + 6\hat{k} = \alpha(2\vec{p} + \vec{q}) + \beta(\vec{p} - 2\vec{q}) + \gamma(\vec{p} \times \vec{q}),
15
i
^
+
10
j
^
+
6
k
^
=
α
(
2
p
+
q
)
+
β
(
p
−
2
q
)
+
γ
(
p
×
q
)
,
then the value of
γ
\gamma
γ
is ________.
Browse the problem library