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Byju's Answer
Standard XII
Mathematics
Equation of Plane Containing Two Lines
If A⃗=1,1,1...
Question
If
→
A
=
(
1
,
1
,
1
)
and
→
C
=
(
0
,
1
,
−
1
)
are given vectors, then vector
→
B
satisfying the equation
→
A
×
→
B
=
→
C
and
→
A
.
→
B
=
3
is
−
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Solution
Let
→
B
=
x
^
i
−
y
^
j
+
z
^
k
According to question
→
A
.
→
B
=
3
⇒
x
+
y
+
z
=
3
Also,
→
A
×
→
B
=
→
C
⇒
∣
∣ ∣
∣
i
j
k
1
1
1
x
y
z
∣
∣ ∣
∣
=
^
j
−
^
k
⇒
i
(
z
−
y
)
−
j
(
z
−
x
)
+
k
(
y
−
x
)
=
^
j
−
^
k
Comparing coefficients
z
−
y
=
0
⇒
z
=
y
z
−
x
=
−
1
⇒
z
=
x
−
1
y
−
x
=
1
⇒
x
−
1
+
x
−
1
+
x
=
3
⇒
3
x
−
2
=
3
⇒
x
=
5
3
∴
y
=
2
3
=
z
∴
→
B
=
5
3
^
i
+
2
3
^
j
+
2
3
^
k
⇒
→
B
=
(
5
3
,
2
3
,
2
3
)
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0
Similar questions
Q.
If
→
A
=
(
1
,
1
,
1
)
,
→
C
=
(
0
,
1
,
−
1
)
are given vectors, then a vector
→
B
satisfying the equation
→
A
×
→
B
=
→
C
and
→
A
.
→
B
=
3
is :
Q.
If
→
A
= (1,1,1) and
→
C
= (0,1,1) are given vectors, then find a vector
→
B
satisfying the equation
→
A
×
→
B
=
→
C
a
n
d
→
A
.
→
B
=
3
Q.
If
→
a
,
→
b
,
→
c
are unit vectors and
→
b
,
→
c
are non-collinear vectors satisfying
(
→
a
,
→
b
)
=
α
,
(
→
a
,
→
c
)
=
β
and
→
a
×
(
→
b
×
→
c
)
=
→
b
+
→
c
2
then
c
o
s
(
α
+
β
)
=
Q.
If
→
a
,
→
b
,
→
c
are vectors such that
→
a
.
→
b
=
0
and
→
a
+
→
b
=
→
c
, then
Q.
Let
→
a
=
→
i
+
→
j
+
→
k
,
→
c
=
→
j
−
→
k
. If
→
b
is a vector satisfying
→
a
×
→
b
=
→
c
and
→
a
.
→
b
=
3
, then
→
b
is
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