1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Addition of Vectors
If a →, b → a...
Question
If
a
→
,
b
→
are two vectors such that
a
→
+
b
→
=
b
→
, then prove that
a
→
+
2
b
→
is perpendicular to
a
→
.
Open in App
Solution
Given that
a
→
+
b
→
=
b
→
Squaring both sides, we get
a
→
+
b
→
2
=
b
→
2
⇒
a
→
2
+
b
→
2
+
2
a
→
.
b
→
=
b
→
2
⇒
a
→
2
+
2
a
→
.
b
→
=
0
.
.
.
1
Now,
a
→
+
2
b
→
.
a
→
=
a
→
.
a
→
+
2
b
→
.
a
→
=
a
→
2
+
2
a
→
.
b
→
=
0
Using
1
So,
a
→
+
2
b
→
is perpendicular to
a
→
.
Suggest Corrections
0
Similar questions
Q.
If
→
a
and
→
b
are two vectors such that
|
→
a
+
→
b
|
=
|
→
a
|
, then prove that vector
2
→
a
+
→
b
is perpendicular to vector
→
b
.
Q.
If
→
a
and
→
b
are two unit vectors such that
→
a
+
2
→
b
and
5
→
a
−
4
→
b
are perpendicular to each other, then the angle between
→
a
and
→
b
is
Q.
If
a
,
→
b
,
→
c
→
are three mutually perpendicular unit vectors, then prove that
a
→
+
b
→
+
c
→
=
3
.
Q.
If
∣
∣
∣
→
a
+
→
b
∣
∣
∣
=
∣
∣
∣
→
a
−
→
b
∣
∣
∣
,
then prove that
→
a
and
→
b
are mutually perpendicular vectors.
Q.
Let
→
a
and
→
b
be two unit vectors such that
|
→
a
+
→
b
|
=
√
3
.
If
→
c
=
→
a
+
2
→
b
+
3
(
→
a
×
→
b
)
,
then
2
|
→
c
|
is equal to:
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 Addition
MATHEMATICS
Watch in App
Explore more
Addition of Vectors
Standard XII Mathematics
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