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Byju's Answer
Standard XII
Mathematics
Vector Triple Product
Show that the...
Question
Show that the vectors
2
i
^
-
3
j
^
+
4
k
^
and
-
4
i
^
+
6
j
^
-
8
k
^
are collinear.
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Solution
Given the position vectors
2
i
^
-
3
j
^
+
4
k
^
and
-
4
i
^
+
6
j
^
-
8
k
^
Let
a
→
=
2
i
^
-
3
j
^
+
4
k
^
and
b
→
=
-
4
i
^
+
6
j
^
-
8
k
^
Then,
b
→
=
-
4
i
^
+
6
j
^
-
8
k
^
=
-
2
2
i
^
-
3
j
^
+
4
k
^
=
-
2
a
→
Hence,
a
→
,
b
→
are collinear.
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Similar questions
Q.
Show that the vectors
2
ˆ
i
−
3
ˆ
j
+
4
ˆ
k
and
−
4
ˆ
i
+
6
ˆ
j
−
8
ˆ
k
are collinear.
Q.
The vectors
2
ˆ
i
−
3
ˆ
j
+
4
ˆ
k
and
−
4
ˆ
i
+
6
ˆ
j
−
8
ˆ
k
are collinear.
Q.
For what value of 'a' the vectors
2
i
^
-
3
j
^
+
4
k
^
and
a
i
^
+
6
j
^
-
8
k
^
are collinear?
Q.
Show the each of the following triads of vectors are coplanar:
(i)
a
→
=
i
^
+
2
j
^
-
k
^
,
b
→
=
3
i
^
+
2
j
^
+
7
k
^
,
c
→
=
5
i
^
+
6
j
^
+
5
k
^
(ii)
a
→
=
-
4
i
^
-
6
j
^
-
2
k
^
,
b
→
=
-
i
^
+
4
j
^
+
3
k
^
,
c
→
=
-
8
i
^
-
j
^
+
3
k
^
(iii)
a
^
=
i
^
-
2
j
^
+
3
k
^
,
b
^
=
-
2
i
^
+
3
j
^
-
4
k
^
,
c
^
=
i
^
-
3
j
^
+
5
k
^
Q.
If
4
ˆ
i
+
7
ˆ
j
+
8
ˆ
k
,
2
ˆ
i
+
3
ˆ
j
+
4
ˆ
k
and
2
ˆ
i
+
5
ˆ
j
+
7
ˆ
k
are the position vectors of the vertices
A
,
B
, and
C
respectively of triangle
A
B
C
, then the position vector of the point where the bisector of angle
A
meets
B
C
is
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