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JEE Advanced 2012 Paper 2 Mathematics Q3
Mathematics
Problem
If
a
⃗
\vec a
a
and
b
⃗
\vec b
b
are vectors such that
∣
a
⃗
+
b
⃗
∣
=
29
|\vec a+\vec b|=\sqrt{29}
∣
a
+
b
∣
=
29
and
a
⃗
×
(
2
i
^
+
3
j
^
+
4
k
^
)
=
(
2
i
^
+
3
j
^
+
4
k
^
)
×
b
⃗
\vec a\times(2\hat i+3\hat j+4\hat k)=(2\hat i+3\hat j+4\hat k)\times\vec b
a
×
(
2
i
^
+
3
j
^
+
4
k
^
)
=
(
2
i
^
+
3
j
^
+
4
k
^
)
×
b
, then a possible value of
(
a
⃗
+
b
⃗
)
⋅
(
−
7
i
^
+
2
j
^
+
3
k
^
)
(\vec a+\vec b)\cdot(-7\hat i+2\hat j+3\hat k)
(
a
+
b
)
⋅
(
−
7
i
^
+
2
j
^
+
3
k
^
)
is
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