Byju's Answer
Standard XII
Mathematics
Conjugate Hyperbola
Find magnitud...
Question
Find magnitude of p if 2i - j + k, i + 3j - 3k and 3i - pj + 5k are co planar
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Q.
Find the value of λ so that the following vectors are coplanar:
(i)
a
→
=
i
^
-
j
^
+
k
^
,
b
→
=
2
i
^
+
j
^
-
k
^
,
c
→
=
λ
i
^
-
j
^
+
λ
k
^
(ii)
a
→
=
2
i
^
-
j
^
+
k
^
,
b
→
=
i
^
+
2
j
^
-
3
k
^
,
c
→
=
λ
i
^
+
λ
j
^
+
5
k
^
(iii)
a
→
=
i
^
+
2
j
^
-
3
k
^
,
b
→
=
3
i
^
+
λ
j
^
+
k
^
,
c
→
=
i
^
+
2
j
^
+
2
k
^
(iv)
a
→
=
i
^
+
3
j
^
,
b
→
=
5
k
^
,
c
→
=
λ
i
^
-
j
^
Q.
Prove that the following vectors are coplanar:
(i)
2
i
^
-
j
^
+
k
^
,
i
^
-
3
j
^
-
5
k
^
and
3
i
^
-
4
j
^
-
4
k
^
(ii)
i
^
+
j
^
+
k
^
,
2
i
^
+
3
j
^
-
k
^
and
-
i
^
-
2
j
^
+
2
k
^
Q.
Find
a
→
b
→
c
→
, when
(i)
a
→
=
2
i
^
-
3
j
^
,
b
→
=
i
^
+
j
^
-
k
^
and
c
→
=
3
i
^
-
k
^
(ii)
a
→
=
i
^
-
2
j
^
+
3
k
^
,
b
→
=
2
i
^
+
j
^
-
k
^
and
c
→
=
j
^
+
k
^
(iii)
a
→
=
2
i
^
+
3
j
^
+
k
^
,
b
→
=
i
^
-
2
j
^
+
k
^
and
c
→
=
-
3
i
^
+
j
^
+
2
k
^
Q.
Find the area of the parallelogram determined by the vectors:
(i)
2
i
^
and
3
j
^
(ii)
2
i
^
+
j
^
+
3
k
^
and
i
^
-
j
^
(iii)
3
i
^
+
j
^
-
2
k
^
and
i
^
-
3
j
^
+
4
k
^
(iv)
i
^
-
3
j
^
+
k
^
and
i
^
+
j
^
+
k
^
.
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
^
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