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Mathematics
Problem
JEE Main 2024 (06 Apr Shift 1) Let
a
⃗
=
2
i
^
−
3
j
^
+
4
k
^
\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}
a
=
2
i
^
−
3
j
^
+
4
k
^
,
b
⃗
=
3
i
^
+
4
j
^
−
5
k
^
\vec{b} = 3\hat{i} + 4\hat{j} - 5\hat{k}
b
=
3
i
^
+
4
j
^
−
5
k
^
and a vector
c
⃗
\vec{c}
c
be such that
a
⃗
×
(
b
⃗
+
c
⃗
)
+
b
⃗
×
c
⃗
=
i
^
+
8
j
^
+
13
k
^
\vec{a} \times (\vec{b} + \vec{c}) + \vec{b} \times \vec{c} = \hat{i} + 8\hat{j} + 13\hat{k}
a
×
(
b
+
c
)
+
b
×
c
=
i
^
+
8
j
^
+
13
k
^
. If
a
⃗
⋅
c
⃗
=
13
\vec{a} \cdot \vec{c} = 13
a
⋅
c
=
13
, then
(
24
−
b
⃗
⋅
c
⃗
)
(24 - \vec{b} \cdot \vec{c})
(
24
−
b
⋅
c
)
is equal to ____.
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