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Byju's Answer
Standard XII
Mathematics
Definition of Vector
If O̅A̅ = 3...
Question
If
¯
O
A
=
3
^
i
+
^
j
−
2
^
k
and
¯
O
B
=
5
^
i
+
4
^
j
−
^
k
then find the value of
¯
A
B
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Solution
To find the value of
→
A
B
If
→
O
A
=
3
ˆ
i
+
ˆ
j
−
2
ˆ
k
,
→
O
B
=
5
ˆ
i
+
4
ˆ
j
−
ˆ
k
Since ,
→
A
B
=
→
O
B
−
→
O
A
→
A
B
=
[
5
ˆ
i
+
4
ˆ
j
−
ˆ
k
]
−
[
3
ˆ
i
+
ˆ
j
−
2
ˆ
k
]
→
A
B
=
5
ˆ
i
+
4
ˆ
j
−
ˆ
k
−
3
ˆ
i
−
ˆ
j
+
2
ˆ
k
→
A
B
=
2
ˆ
i
+
3
ˆ
j
+
ˆ
k
Hence ,
→
A
B
=
2
ˆ
i
+
3
ˆ
j
+
ˆ
k
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Similar questions
Q.
The distance between the parallel lines
→
r
=
2
^
i
+
3
^
j
−
^
k
+
λ
(
^
i
−
^
j
+
2
^
k
)
and
→
r
=
−
3
^
i
+
4
^
j
+
^
k
+
μ
(
^
i
−
^
j
+
2
^
k
)
is
Q.
I: If
→
a
=
3
^
i
−
2
^
j
+
^
k
,
→
b
=
2
^
i
−
4
^
j
−
3
^
k
,
→
c
=
−
^
i
+
2
^
j
+
2
^
k
then
→
a
+
→
b
+
→
c
=
4
^
i
−
4
^
j
II: If
→
a
=
^
i
−
^
j
+
2
^
k
,
→
b
=
2
^
i
+
3
^
j
+
^
k
,
→
c
=
^
i
−
^
k
, then magnitude of
→
a
+
2
→
b
−
3
→
c
is
√
78
Q.
The position vectors of the points
A
,
B
,
C
and
D
are
3
^
i
−
2
^
j
−
^
k
,
2
^
i
−
3
^
j
+
2
^
k
,
5
^
i
−
^
j
+
2
^
k
and
4
^
i
−
^
j
+
λ
^
k
respectively. If the points
A
,
B
,
C
and
D
lie on a plane, the find the value of
λ
?
Q.
If
→
a
=
3
^
j
−
2
^
j
+
7
^
k
,
→
b
=
5
^
i
+
^
j
−
2
^
k
and
→
c
=
^
i
+
^
j
−
^
k
, then find
→
a
⋅
(
→
b
×
→
c
)
.
Q.
The line of intersection of the planes
→
r
⋅
(
3
^
i
−
^
j
+
^
k
)
=
1
and
→
r
⋅
(
^
i
+
4
^
j
−
2
^
k
)
=
2
, is.
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