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JEE Main Math Class 12 Vector Algebra Questions Part 2 Questions
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© examsnet.com
Question : 2
Total: 100
Let :
→
a
=
^
i
+
2
^
j
+
3
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
and
→
c
=
5
^
i
−
3
^
j
+
3
^
k
be there vectors. If
→
r
is a vector such that,
→
r
×
→
b
=
→
c
×
→
b
and
→
r
⋅
→
a
=
0
. Then
25
|
→
r
|
2
is equal to
[31-Jan-2023 Shift 2]
449
336
339
560
Validate
Solution:
Sol.
→
a
=
i
+
2
j
+
3
k
→
b
=
i
−
j
+
2
k
→
c
=
^
5
i
−
3
^
j
+
3
^
k
(
→
r
−
→
c
)
×
→
b
=
0
,
→
r
⋅
→
a
=
0
⇒
→
r
−
→
c
=
λ
→
b
Also,
(
→
c
+
λ
→
b
)
⋅
→
a
=
0
⇒
→
a
⋅
→
c
+
λ
(
→
a
⋅
→
b
)
=
0
∴
λ
=
→
a
⋅
→
c
→
a
⋅
→
b
=
−
8
5
→
r
=
5
(
5
^
i
−
3
^
i
+
3
^
k
)
−
8
(
^
i
−
^
j
+
2
^
k
)
5
→
r
=
17
^
i
−
7
^
j
+
^
k
5
|
→
r
|
2
=
1
25
(
289
+
50
)
25
|
→
r
|
2
=
339
© examsnet.com
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