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Byju's Answer
Standard XII
Mathematics
Vector Equation for Straight Line
let a=i+j,b=j...
Question
let a=i+j,b=j+k and c=αa+βb.If the vectors i-2j+k, 3i+2j-k and c are coplanar then α/β equals
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Similar questions
Q.
If
→
a
=
→
i
+
2
→
j
+
3
→
k
,
→
b
=
2
→
i
+
3
→
j
+
→
k
,
→
c
=
3
→
i
+
→
j
+
2
→
k
and
α
→
a
+
β
→
b
+
γ
→
c
=
−
3
(
ˆ
i
−
ˆ
k
)
, then the order triplet
(
α
,
β
,
γ
)
is
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 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.
Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
(i)
a
→
=
2
i
^
+
3
j
^
+
4
k
^
,
b
→
=
i
^
+
2
j
^
-
k
^
,
c
→
=
3
i
^
-
j
^
+
2
k
^
(ii)
a
→
=
2
i
^
-
3
j
^
+
4
k
^
,
b
→
=
i
^
+
2
j
^
-
k
^
,
c
→
=
3
i
^
-
j
^
-
2
k
^
(iii)
a
→
=
11
i
^
,
b
→
=
2
j
^
,
c
→
=
13
k
^
(iv)
a
→
=
i
^
+
j
^
+
k
^
,
b
→
=
i
^
-
j
^
+
k
^
,
c
→
=
i
^
+
2
j
^
-
k
^
Q.
If
a
→
=
i
^
+
j
^
-
k
^
,
b
→
=
-
i
^
+
2
j
^
+
2
k
^
and
c
→
=
-
i
^
+
2
j
^
-
k
^
,
then a unit vector normal to the vectors
a
→
+
b
→
and
b
→
-
c
→
is
(a)
i
^
(b)
j
^
(c)
k
^
(d) none of these
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