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Byju's Answer
Standard XII
Mathematics
Dot Product
Given three p...
Question
Given three points whose position vectors are
x
ˆ
i
+
y
ˆ
j
+
z
ˆ
k
,
ˆ
i
+
z
ˆ
j
and
ˆ
i
−
ˆ
j
find the condition for the points to be collinear,
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Solution
Given,
x
ˆ
i
+
y
ˆ
j
+
z
ˆ
k
ˆ
i
+
z
ˆ
j
ˆ
i
−
ˆ
j
a
r
e
c
o
l
l
i
n
e
a
r
.
S
o
,
⎛
⎜
⎝
x
y
z
a
1
z
0
1
−
1
0
⎞
⎟
⎠
=
0
x
(
0
)
−
y
(
0
)
+
z
(
−
1
−
z
)
=
0
∴
z
=
0
a
n
d
z
=
−
1
i
f
z
=
0
a
n
d
z
=
−
1
s
o
,
f
o
r
a
l
l
x
,
y
t
h
e
s
e
v
e
c
t
o
r
s
a
r
e
c
o
l
l
i
n
e
a
r
.
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0
Similar questions
Q.
The vectors
a
=
x
i
−
2
j
+
5
k
and
b
=
i
+
y
j
−
z
k
are collinear if
Q.
The vectors
x
i
−
3
j
+
7
k
and
i
+
y
j
−
z
k
are collinear then the value of
x
y
2
z
=
Q.
The position vector of a point
P
is
r
=
x
i
+
y
j
+
z
k
,
where
x
,
y
,
z
∈
N
and
u
=
i
+
j
+
k
.
If
r
⋅
u
=
10
, then the possible positions of
P
are
Q.
If
¯
¯
¯
r
=
x
¯
i
+
y
¯
j
+
z
¯
¯
¯
k
, then
(
¯
¯
¯
r
×
¯
i
)
.
(
¯
¯
¯
r
×
¯
j
)
=
Q.
The position vector of P,
¯
O
P
=
x
i
+
y
j
+
z
k
where
x
,
y
,
z
∈
N
and a
=
i
+
j
+
k
. If
¯
O
P
.
a
=
18 then the number of possible positions of P is
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