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Mathematics
Let vec a =2 hati-7 hatj+5 hatk, vec b = hati+ hatk and vec c = hati+2 hatj-3 hatk be three given vectors. If vec r is a vector such that vecr × veca= vecc × veca and vecr ⋅ vecb=0, then | vecr| is equal to :
Q. Let
a
=
2
i
^
−
7
j
^
+
5
k
^
,
b
=
i
^
+
k
^
and
c
=
i
^
+
2
j
^
−
3
k
^
be three given vectors. If
r
is a vector such that
r
×
a
=
c
×
a
and
r
⋅
b
=
0
, then
∣
r
∣
is equal to :
209
137
JEE Main
JEE Main 2023
Vector Algebra
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A
7
11
2
100%
B
7
11
0%
C
7
914
0%
D
5
11
2
0%
Solution:
a
=
2
i
^
−
7
j
^
+
5
k
^
b
=
i
^
+
k
^
c
=
i
^
+
2
j
^
−
3
k
^
r
×
a
=
c
×
a
⇒
(
r
−
c
)
×
a
=
0
∴
r
=
c
+
λ
a
r
⋅
b
=
0
⇒
c
⋅
b
+
λ
b
⋅
a
=
0
−
2
+
λ
(
7
)
=
0
⇒
λ
=
7
2
∴
r
=
c
+
7
2
a
=
7
1
(
11
i
^
−
11
k
^
)
∣
r
=
7
11
2