Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
x
0
x_0
x
0
be the point of local maxima of
f
(
x
)
=
a
⃗
⋅
(
b
⃗
×
c
⃗
)
f(x) = \vec{a} \cdot (\vec{b} \times \vec{c})
f
(
x
)
=
a
⋅
(
b
×
c
)
, where
a
⃗
=
x
i
^
−
2
j
^
+
3
k
^
\vec{a} = x\hat{i} - 2\hat{j} + 3\hat{k}
a
=
x
i
^
−
2
j
^
+
3
k
^
,
b
⃗
=
−
2
i
^
+
x
j
^
−
k
^
\vec{b} = -2\hat{i} + x\hat{j} - \hat{k}
b
=
−
2
i
^
+
x
j
^
−
k
^
and
c
⃗
=
7
i
^
−
2
j
^
+
x
k
^
\vec{c} = 7\hat{i} - 2\hat{j} + x\hat{k}
c
=
7
i
^
−
2
j
^
+
x
k
^
. Then the value of
a
⃗
⋅
b
⃗
+
b
⃗
⋅
c
⃗
+
c
⃗
⋅
a
⃗
\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}
a
⋅
b
+
b
⋅
c
+
c
⋅
a
at
x
=
x
0
x = x_0
x
=
x
0
is : [JEE MAINS - ONLINE - 2020] 1. -30 2. 14 3. -4 4. -22
Browse the problem library