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Byju's Answer
Standard XII
Mathematics
Applications of Dot Product
Show that the...
Question
Show that the points with position vectors
−
^
i
+
6
^
j
+
6
^
k
,
−
4
^
i
+
9
^
j
+
6
^
k
,
and
7
^
j
+
10
^
k
from a right angled triangle.
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Solution
A
(
−
ˆ
i
+
6
ˆ
j
+
6
ˆ
k
)
B
(
−
4
ˆ
i
+
9
ˆ
j
+
6
ˆ
k
)
C
(
7
ˆ
j
+
10
ˆ
k
)
−
−
→
A
B
=
−
3
ˆ
i
+
3
ˆ
j
−
−
→
A
C
=
ˆ
i
+
ˆ
j
+
4
ˆ
k
−
−
→
A
B
.
−
−
→
A
C
=
0
T
h
u
s
A
,
B
a
n
d
C
f
o
r
a
n
r
i
g
h
t
a
n
g
l
e
d
t
r
i
a
n
g
l
e
.
Suggest Corrections
0
Similar questions
Q.
Let
A
B
C
be a triangle, the position vector of whose vertices are respectively
−
10
^
i
+
10
^
k
,
−
^
i
+
6
^
j
+
6
^
k
and
−
4
^
i
+
9
^
j
+
6
^
k
then
△
A
B
C
is
Q.
Show that the four points whose position vectors are
6
^
i
−
7
^
j
,
16
^
i
−
29
^
j
−
4
^
k
,
3
^
j
−
6
^
k
and
2
^
i
+
5
^
j
+
10
^
k
are coplanar.
Q.
The position vectors of points
A
,
B
,
C
and
D
are
A
=
3
^
i
+
4
^
j
+
5
^
k
,
B
=
4
^
i
+
5
^
j
+
6
^
k
,
C
=
7
^
i
+
9
^
j
+
3
^
k
and
D
=
4
^
i
+
6
^
j
, then the displacement vectors
−
−
→
A
B
and
−
−
→
C
D
are
Q.
The position vectors of points
A
,
B
,
C
and
D
are
A
=
3
^
i
+
4
^
j
+
5
^
k
,
B
=
4
^
i
+
5
^
j
+
6
^
k
,
C
=
7
^
i
+
9
^
j
+
3
^
k
and
D
=
4
^
i
+
6
^
j
. Then, the displacement vectors
A
B
and
C
D
are
Q.
The position vectors of points
A
,
B
,
C
and
D
are
A
=
3
^
i
+
4
^
j
+
5
^
k
,
B
=
4
^
i
+
5
^
j
+
6
^
k
,
C
=
7
^
i
+
9
^
j
+
3
^
k
and
D
=
4
^
i
+
6
^
j
. Then, the displacement vectors
A
B
and
C
D
are
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