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Byju's Answer
Standard XII
Mathematics
Definition of Vector
If V⃗1=î-2ĵ...
Question
If
→
V
1
=
^
i
−
2
^
j
+
3
^
k
and
→
V
2
=
a
^
i
+
b
^
j
+
c
^
k
where
a
,
b
,
c
∈
{
−
1
,
0
,
1
,
2
,
3
}
then find the numbers of non-zero vectors
→
V
2
which are normal to
→
V
1
.
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Solution
∵
→
V
2
is normal to
→
V
1
⇒
→
V
1
.
→
V
2
=
0
⇒
(
→
i
−
2
→
j
+
→
k
)
(
a
→
i
+
b
→
j
+
c
→
k
)
=
0
⇒
a
−
2
b
+
3
c
=
0
If
a
=
−
1
,
3
c
−
2
b
=
1
⇒
c
=
1
,
b
=
1
→
1
If
a
=
0
,
3
c
=
2
b
⇒
c
=
0
,
b
=
0
→
2
o
r
c
=
2
,
b
=
3
→
3
If
a
=
1
,
2
b
−
3
c
=
1
⇒
c
=
−
1
,
b
=
−
1
→
4
⇒
b
=
2
,
c
=
1
→
4
If
a
=
2
,
2
b
−
3
c
=
2
⇒
c
=
0
,
b
=
1
→
6
o
r
c
=
2
,
b
=
3
→
3
If
a
=
3
,
2
b
−
3
c
=
3
⇒
c
=
−
1
,
b
=
0
→
7
⇒
b
=
3
,
c
=
1
→
8
∴
8 non-zero vectors
→
V
2
are possible
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0
Similar questions
Q.
Consider three vectors
→
v
1
,
→
v
2
and
→
v
3
such that
→
v
1
=
→
v
2
−
→
v
3
where
→
v
1
=
(
→
a
×
ˆ
i
)
×
ˆ
i
,
→
v
2
=
(
→
a
×
ˆ
j
)
×
ˆ
j
&
→
v
3
=
(
→
a
×
ˆ
k
)
×
ˆ
k
.
(
→
a
is non zero vector), then
Q.
Let
¯
a
,
¯
b
,
¯
c
be three non coplanar vectors. Define
→
v
1
,
→
v
2
,
→
v
3
by
→
v
1
=
→
b
×
→
c
[
→
a
→
b
→
c
]
,
→
v
2
=
→
c
×
→
a
[
→
a
→
b
→
c
]
,
→
v
3
=
→
a
×
→
b
[
→
a
→
b
→
c
]
which of the following statements is false?
Q.
The angle between
→
V
1
=
^
i
+
2
^
j
+
2
^
k
and
→
V
2
=
2
^
i
+
3
^
j
−
4
^
k
is:
Q.
If
→
p
=
^
i
+
^
j
+
^
k
and
→
q
=
a
^
i
+
b
^
j
+
c
^
k
where
a
,
b
,
c
→
{
−
2
,
−
1
,
0
,
1
,
2
}
. then the number of vectors
→
q
is perpendicular to
→
a
is
Q.
An impulse
→
1
changes the velocity of a particle from
→
v
1
to
→
v
2
. Kinetic energy gained by the particle is
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