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JEE Main Math Class 12 Vector Algebra Part 3 Questions
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© examsnet.com
Question : 7
Total: 70
Let
→
a
=
2
^
i
+
5
^
j
−
^
k
,
→
b
=
2
^
i
−
2
^
j
+
2
^
k
and
→
c
be three vectors such that
(
→
c
+
^
i
)
×
(
→
a
+
→
b
+
^
i
)
=
→
a
×
(
→
c
+
^
i
)
⋅
→
a
⋅
→
c
=
−
29
,
then
→
c
⋅
(
−
2
^
i
+
^
j
+
^
k
)
is equal to :
[5 Apr 2024 Shift 2]
10
5
15
12
Validate
Solution:
👈: Video Solution
Let's assume
→
v
=
→
a
+
→
b
+
^
i
=
5
^
i
+
3
^
j
+
^
k
and
→
c
+
^
i
=
→
p
So,
→
p
×
→
v
=
→
a
×
→
p
→
p
×
→
v
+
→
p
×
→
a
=
→
0
→
p
×
(
→
v
+
→
a
)
=
→
0
⇒
→
p
=
λ
(
→
v
+
→
a
)
→
c
+
i
=
λ
(
7
^
i
+
8
^
j
)
a
⋅
c
+
a
⋅
^
i
=
λ
a
⋅
(
7
^
i
+
8
^
j
)
−
29
+
2
=
λ
(
14
+
40
)
λ
=
−
1
2
→
c
⋅
(
−
2
^
i
+
^
j
+
^
k
)
+
^
i
⋅
(
−
2
^
i
+
^
j
+
^
k
)
=
λ
(
7
^
i
+
8
^
j
)
⋅
(
−
2
^
i
+
^
j
+
^
k
)
=
−
1
2
(
−
14
+
8
)
+
2
=
5
© examsnet.com
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