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Byju's Answer
Standard XII
Mathematics
Linear Dependence and Independence of Vectors
Solve questio...
Question
Solve question 7 and no links.
7. Find a vector of magnitude 18 which is perpendicular to both the vectors
4
i
^
-
j
^
+
3
k
^
a
n
d
-
2
i
^
+
j
^
-
2
k
^
.
(Ans.
-
6
i
^
+
12
j
^
+
12
k
^
)
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Solution
Dear Student,
a
⇀
=
4
i
^
-
j
^
+
3
k
^
b
⇀
=
-
2
i
^
+
j
^
-
2
k
^
f
i
n
d
a
×
b
t
h
e
v
e
c
t
o
r
t
h
a
t
c
o
m
e
s
w
i
l
l
b
e
p
e
r
p
e
n
d
i
c
u
l
a
r
t
o
b
o
t
h
a
a
n
d
b
a
⇀
×
b
⇀
=
i
j
k
4
-
1
3
-
2
1
-
2
=
i
2
-
3
-
j
-
8
+
6
+
k
4
-
2
=
-
i
^
+
2
j
^
+
2
k
^
u
n
i
t
v
e
c
t
o
r
i
n
t
h
i
s
d
i
r
e
c
t
i
o
n
=
-
i
^
+
2
j
^
+
2
k
^
1
+
4
+
4
=
-
i
^
+
2
j
^
+
2
k
^
3
v
e
c
t
o
r
o
f
m
a
g
n
i
t
u
d
e
18
a
n
d
p
e
r
p
e
n
d
i
c
u
l
a
r
t
o
b
o
t
h
t
h
e
v
e
c
t
o
r
=
18
-
i
^
+
2
j
^
+
2
k
^
3
=
-
6
i
^
+
12
j
^
+
12
k
^
R
e
g
a
r
d
s
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0
Similar questions
Q.
(i) Find a unit vector perpendicular to both the vectors
4
i
^
-
j
^
+
3
k
^
and
-
2
i
^
+
j
^
-
2
k
^
.
(ii) Find a unit vector perpendicular to the plane containing the vectors
a
→
=
2
i
^
+
j
^
+
k
^
and
b
→
=
i
^
+
2
j
^
+
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^
.
Q.
(i) Find a vector of magnitude 49, which is perpendicular to both the vectors
2
i
^
+
3
j
^
+
6
k
^
and
3
i
^
-
6
j
^
+
2
k
^
.
(ii) Find a vector whose length is 3 and which is perpendicular to the vector
a
→
=
3
i
^
+
j
^
-
4
k
^
and
b
→
=
6
i
^
+
5
j
^
-
2
k
^
.
Q.
The vector equation of a plane through the point
(
2
ˆ
i
−
ˆ
j
−
4
ˆ
k
)
and parallel to the plane
→
r
.
(
4
ˆ
i
−
12
ˆ
j
−
3
ˆ
k
)
−
7
=
0
is
Q.
Find a vector of magnitude
171
which is perpendicular to both of the vectors
a
→
=
i
^
+
2
j
^
-
3
k
^
and
b
→
=
3
i
^
-
j
^
+
2
k
^
.
Q.
The unit vector in the direction of sum of the vectors
→
A
=
2
ˆ
i
+
4
ˆ
j
−
7
ˆ
k
and
→
B
=
4
ˆ
i
−
6
ˆ
j
+
4
ˆ
k
will be