Solve
Study
Textbooks
Guides
Join / Login
>>
Class 11
>>
Physics
>>
Motion in a Plane
>>
Mathematical Operations on Vectors
>>
Unit vector n = avec i + bvec j is perpe
Question
Unit vector
n
=
a
i
^
+
b
j
^
is perpendicular to the vector
(
i
^
+
j
^
)
, then the value of a and b may be:
A
1
,
0
B
−
2
,
0
C
3
,
0
D
2
1
,
−
2
1
Medium
Open in App
Solution
Verified by Toppr
Correct option is D)
Since
(
a
i
^
+
b
j
^
)
⊥
(
i
^
+
j
^
)
Let
i
^
+
j
^
=
B
Also we know dot product of two vectors =0
Thus
(
a
i
^
+
b
j
^
)
.
(
i
^
+
j
^
)
=
0
a
+
b
=
0
a
=
−
b
-----------(1)
As we know n=1 as n is a unit vector
∣
n
∣
=
a
2
+
b
2
=
1
a
2
+
b
2
=
1
(
−
b
)
2
+
b
2
=
1
b
=
2
1
and
a
=
2
−
1
Solve any question of
Motion in a Plane
with:-
Patterns of problems
>
Was this answer helpful?
0
0
Similar questions
Magnitude of vector
i
^
−
j
^
.
Easy
View solution
>
The angle between
A
=
i
^
+
2
j
^
−
k
^
and
B
=
−
i
^
+
j
^
−
2
k
^
is
Medium
View solution
>
Find the vector that must be added to the vector
i
^
−
3
j
^
+
2
k
^
and
3
i
^
+
6
j
^
−
7
k
^
so that the resultant vector is a unit vector along the
y
- axis.
Hard
View solution
>
When a vector
A
=
−
2
i
^
+
4
j
^
+
7
k
^
is multiplied with a scalar
′
n
′
, the resultant vector is
4
i
^
−
8
j
^
−
1
4
k
^
. Then the value of
′
n
′
, is
Medium
View solution
>
A unit vector in the direction of resultant vector of
A
= -2
i
^
+3
j
^
+
k
^
and
B
=
i
^
+2
j
^
-4
k
^
is
Medium
View solution
>
View more
More From Chapter
Motion in a Plane
View chapter
>
Revise with Concepts
Addition and Subtraction of Vectors
Example
Definitions
Formulaes
Law of Sines and Law of Cosines and Use in Vector Addition
Example
Definitions
Formulaes
Resolution of Vectors
Example
Definitions
Formulaes
Unit Vector
Example
Definitions
Formulaes
Multiplication of a Vector by a Scalar
Example
Definitions
Formulaes
Vector Addition by Component Method
Example
Definitions
Formulaes
View more
Learn with Videos
Addition of vectors
5 mins
Triangular Law of Vector Addition - Graphical Method
7 mins
Resultant of Two Vectors - 1
7 mins
Resultant of Two Vectors - 2
7 mins
Parallelogram Law of Vector Addition
16 mins
Polygon Law of Vector Addition
3 mins
Properties of Addition of Vectors
6 mins
Laws of Vector Addition-I
19 mins
Laws of Vector Addition - II
20 mins
Representation of Vector in Rectangular Coordinate System
18 mins
Finding unit vector perpendicular to two given vectors
8 mins
Product of Vector with Scalar
4 mins
Multiplication of vectors by a scalar
7 mins
Vector Addition in Rectangular Coordinate System
4 mins
Component of Vectors
28 mins
Resultant of 3 or More Vectors
9 mins
Shortcuts & Tips
Mindmap
>
Problem solving tips
>
Common Misconceptions
>
Important Diagrams
>
Cheatsheets
>
Memorization tricks
>
Practice more questions
JEE Mains Questions
3 Qs
>
JEE Advanced Questions
1 Qs
>
NEET Questions
2 Qs
>
AIIMS Questions
1 Qs
>
Easy Questions
130 Qs
>
Medium Questions
588 Qs
>