1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Physics
Vector Component
Let a⃗ = î ...
Question
Let
→
a
=
^
i
+
4
^
j
+
2
^
k
,
→
b
=
3
^
i
−
2
^
j
+
7
^
k
and
→
c
=
2
^
i
−
^
j
+
4
^
k
. Find a vector
→
p
which is perpendicular to both
→
a
and
→
b
and
→
p
⋅
→
c
=
18.
Open in App
Solution
→
a
=
^
i
+
4
^
j
+
2
^
k
,
→
b
=
3
^
i
−
2
^
j
+
7
^
k
Since we need a vector perpendicular to both
→
a
and
→
b
, it has to be parallel to
→
a
×
→
b
→
a
×
→
b
=
(
^
i
+
4
^
j
+
2
^
k
)
×
(
3
^
i
−
2
^
j
+
7
^
k
)
=
−
2
^
k
−
7
^
j
−
12
^
k
+
28
^
i
+
6
^
j
+
4
^
i
=
32
^
i
−
^
j
−
14
^
k
The unit vector in this direction can be written as
32
^
i
−
^
j
−
14
^
k
√
1024
+
1
+
196
=
32
^
i
−
^
j
−
14
^
k
√
1221
Since
→
p
.
→
c
=
18
,
∴
k
√
1221
×
(
32
^
i
−
^
j
−
14
^
k
)
.
(
2
^
i
−
^
j
+
4
^
k
)
=
18
∴
k
√
1221
×
(
64
+
1
−
56
)
=
18
∴
k
=
2
√
1221
∴
→
p
=
k
√
1221
×
(
32
^
i
−
^
j
−
14
^
k
)
=
2
×
(
32
^
i
−
^
j
−
14
^
k
)
=
64
^
i
−
2
^
j
−
28
^
k
Suggest Corrections
0
Similar questions
Q.
If
→
a
=
^
i
+
4
^
j
+
2
^
k
,
→
b
=
3
^
i
−
2
^
j
+
7
^
k
and
→
c
=
2
^
i
−
^
j
+
4
^
k
, then find a vector
→
d
which is perpendicular to both
→
a
and
→
b
and
→
c
⋅
→
d
=
15
Q.
I: If
→
a
=
3
^
i
−
2
^
j
+
^
k
,
→
b
=
2
^
i
−
4
^
j
−
3
^
k
,
→
c
=
−
^
i
+
2
^
j
+
2
^
k
then
→
a
+
→
b
+
→
c
=
4
^
i
−
4
^
j
II: If
→
a
=
^
i
−
^
j
+
2
^
k
,
→
b
=
2
^
i
+
3
^
j
+
^
k
,
→
c
=
^
i
−
^
k
, then magnitude of
→
a
+
2
→
b
−
3
→
c
is
√
78
Q.
Let
→
a
=
2
^
i
−
3
^
j
+
4
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
and
→
c
=
6
^
i
−
3
^
j
+
^
k
, then find
→
d
which is perpendicular to both
→
a
and
→
b
and
→
c
.
→
d
=
2
Q.
Let
→
a
=
4
^
i
+
5
^
j
−
^
k
,
→
b
=
^
i
−
4
^
j
+
5
^
k
,
and
→
c
=
3
^
i
−
^
j
−
^
k
. Find a vector
→
d
which is perpendicular to both
→
c
and
→
b
and
→
d
.
→
a
=
21
.
Q.
Given
→
a
=
^
i
+
^
j
−
^
k
,
→
b
=
−
^
i
+
2
^
j
+
^
k
and
→
c
=
−
^
i
+
2
^
i
−
^
k
.
A
unit vector perpendicular to both
→
a
+
→
b
&
→
b
+
→
c
is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Vector Components
PHYSICS
Watch in App
Explore more
CBSE Board
Vector Component
Standard XII Physics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app