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Byju's Answer
Standard IX
Mathematics
Test for Coplanarity
Show that the...
Question
Show that the vectors
a
=
3
^
i
−
2
^
j
+
^
k
,
b
=
^
i
−
3
^
j
+
5
^
k
and
c
=
2
^
i
+
^
j
−
4
^
k
from a right angled triangle.
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Solution
We have
a
=
(
3
^
i
−
2
^
j
+
^
k
)
,
b
=
(
^
i
−
3
^
j
−
4
^
k
)
and
c
=
(
2
^
i
+
^
j
−
4
^
k
)
Since
b
+
c
=
a
⇒
(
^
i
−
3
^
j
−
4
^
k
)
+
(
2
^
i
+
^
j
−
4
^
k
)
=
(
3
^
i
−
2
^
j
+
^
k
)
so, a, b and c formed a triangle.
Also,
→
a
.
→
c
=
(
3
^
i
−
2
^
j
+
^
k
)
.
(
2
^
i
+
^
j
−
4
^
k
)
=
(
+
6
−
2
−
4
)
=
0
So,
→
a
and
→
c
are perpendicular.
Therefore,
a
,
b
a
n
d
c
form a right angled triangle.
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i
−
2
^
j
+
^
k
)
,
→
b
=
(
^
i
−
3
^
j
+
5
^
k
)
and
→
c
=
(
2
^
i
+
^
j
−
4
^
k
)
have a characteristics to form
Q.
The vectors
3
^
i
−
2
^
j
+
^
k
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i
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j
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and
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