Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
a
⃗
=
i
^
+
j
^
+
k
^
\vec{a} = \hat{i} + \hat{j} + \hat{k}
a
=
i
^
+
j
^
+
k
^
,
b
⃗
=
−
i
^
−
8
j
^
+
2
k
^
\vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}
b
=
−
i
^
−
8
j
^
+
2
k
^
and
c
⃗
=
4
i
^
+
c
2
j
^
+
c
3
k
^
\vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k}
c
=
4
i
^
+
c
2
j
^
+
c
3
k
^
be three vectors such that
b
⃗
×
a
⃗
=
c
⃗
×
a
⃗
\vec{b} \times \vec{a} = \vec{c} \times \vec{a}
b
×
a
=
c
×
a
. If the angle between the vector
c
⃗
\vec{c}
c
and the vector
3
i
^
+
4
j
^
+
k
^
3\hat{i} + 4\hat{j} + \hat{k}
3
i
^
+
4
j
^
+
k
^
is
θ
\theta
θ
, then the greatest integer less than or equal to
tan
2
θ
\tan^2 \theta
tan
2
θ
is:
Browse the problem library