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Byju's Answer
Standard VIII
Mathematics
Polynomials
Find a → b → ...
Question
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
^
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Solution
i
Given
:
a
→
=
2
i
^
-
3
j
^
b
→
=
i
^
+
j
^
-
k
^
c
→
=
3
i
^
-
k
^
∴
a
→
×
b
→
=
2
i
^
-
3
j
^
×
i
^
+
j
^
-
k
^
=
2
k
^
+
2
j
^
+
3
k
^
+
3
i
^
=
3
i
^
+
2
j
^
+
5
k
^
a
→
×
b
→
.
c
→
=
3
i
^
+
2
j
^
+
5
k
^
.
3
i
^
-
k
^
=
9
-
5
=
4
.
.
.
1
Now
,
a
→
b
→
c
→
=
a
→
×
b
→
.
c
→
=
4
Using
1
ii
Given
:
a
→
=
i
^
-
2
j
^
+
3
k
^
b
→
=
2
i
^
+
j
^
-
k
^
c
→
=
j
^
+
k
^
∴
a
→
×
b
→
=
i
^
-
2
j
^
+
3
k
^
×
2
i
^
+
j
^
-
k
^
=
k
^
+
j
^
+
4
k
^
+
2
i
^
+
6
j
^
-
3
i
^
=
-
i
^
+
7
j
^
+
5
k
^
a
→
×
b
→
.
c
→
=
-
i
^
+
7
j
^
+
5
k
^
.
j
^
+
k
^
=
7
+
5
=
12
.
.
.
1
Now
,
a
→
b
→
c
→
=
a
→
×
b
→
.
c
→
=
12
Using
1
Suggest Corrections
0
Similar questions
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.
Find
a
→
·
b
→
when
(i)
a
→
=
i
^
-
2
j
^
+
k
^
and
b
→
=
4
i
^
-
4
j
^
+
7
k
^
(ii)
a
→
=
j
^
+
2
k
^
and
b
→
=
2
i
^
+
k
^
(iii)
a
→
=
j
^
-
k
^
and
b
→
=
2
i
^
+
3
j
^
-
2
k
^
Q.
If
¯
¯
¯
r
×
¯
¯
b
=
¯
¯
c
×
¯
¯
b
.
¯
¯
¯
r
.
¯
¯
¯
a
=
0
,
¯
¯
¯
a
=
2
¯
i
+
3
¯
j
−
¯
¯
¯
k
,
¯
¯
b
=
3
¯
i
−
¯
j
+
¯
¯
¯
k
,
¯
¯
c
=
¯
i
+
¯
j
+
3
¯
¯
¯
k
, then
¯
¯
¯
r
=
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