Toggle navigation
Test.Brainkart.com
Home
GATE Exam
TN School
College Entrance Exam
IIT JEE
NEET
AIIMS
CAT
CLAT
TANCET
10th & 12th
11th Std
12th Std
10th Std
Job Entrance Exam
BANK
UGC NET
TNPSC
Vector Algebra
- Online Test
Vector Algebra
TEST : 5
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q1.
The scalar product of two nonzero vectors
is defined as
A.
B.
C.
D.
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
The scalar product of two nonzero vectors
is defined as :
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q2.
A.
a
1
b
1
−
a
2
b
2
+
a
3
b
3
B.
a
1
b
1
+
a
2
b
2
−
a
3
b
3
C.
a
1
b
1
−
a
2
b
2
−
a
3
b
3
D.
a
1
b
1
+
a
2
b
2
+
a
3
b
3
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q3.
If
θ
θ
is the angle between vectors
a
⃗
a
n
d
b
⃗
then the cross product
a
⃗
×
b
⃗
=
A.
2
|
a
|
|
b
|
sin
θ
n
^
B.
|
a
|
|
b
|
sin
θ
C.
|
a
|
|
b
|
cos
θ
D.
∣
∣
a
→
∣
∣
∣
∣
∣
b
→
∣
∣
∣
sin
θ
n
^
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
If
θ
is the angle between vectors
a
⃗
a
n
d
b
⃗
then, the cross product :
a
⃗
×
b
⃗
=
∣
∣
a
→
∣
∣
∣
∣
∣
b
→
∣
∣
∣
sin
θ
n
^
.
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q4.
Find the unit vector in the direction of the vector
A.
B.
C.
a
→
=
D.
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q5.
If
⃗
a
is a non zero vector of magnitude ‘a’ and
λ
a non zero scalar, then
λ
a
⃗
is a unit vector if
A.
λ=1
B.
λ=−1
C.
a = |λ|
D.
a = 1/|λ|
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
λ
a
⃗
is a unit vector if and only if
⃗
a
is equal to
1
|
λ
|
.
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q6.
A.
19√5
B.
17√2
C.
8√3
D.
19√3
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q7.
Find a unit vector perpendicular to each of
where
A.
∓
2
3
i
^
∓
2
3
j
^
∓
1
3
k
^
B.
±
2
3
i
^
±
2
3
j
^
∓
1
3
k
^
C.
±
2
3
i
^
±
2
3
j
^
±
1
3
k
^
D.
±
1
3
(
2
i
ˆ
−
2
j
ˆ
−
k
ˆ
)
.
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
It is given that:
Therefore, the unit vector perpendicular to both the vectors
(
a
→
+
b
→
)
and
(
a
→
−
b
→
)
is given by:
=
±
(
16
i
ˆ
−
16
j
ˆ
−
8
k
ˆ
)
24
=
±
1
3
(
2
i
ˆ
−
2
j
ˆ
−
k
ˆ
)
.
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q8.
If a unit vector
⃗
a
makes angles
π
3
w
i
t
h
i
^
π
4
w
i
t
h
j
^
a
n
d
a
n
a
c
u
t
e
a
n
g
l
e
θ
w
i
t
h
k
^
, then find
θ
A.
2(π/3)
B.
π/10
C.
π/3
D.
π/5
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
Let
a
→
=
a
1
i
ˆ
+
a
2
j
ˆ
+
a
3
k
ˆ
,
It is given that
∣
∣
a
→
∣
∣
=
1
, then,
Putting these values in (1), we get:
1
4
+
1
2
+
cos
2
θ
=
1
=
1
−
cos
2
θ
⇒
sin
2
θ
=
3
4
⇒
sin
θ
=
3
√
2
⇒
θ
=
60
∘
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q9.
If a unit vector
⃗
a
makes angles
π
3
w
i
t
h
i
^
,
π
4
w
i
t
h
j
^
a
n
d
a
n
a
c
u
t
e
a
n
g
l
e
θ
w
i
t
h
k
^
, then the components of
⃗
a
are
A.
1
3
,
1
3
√
,
1
2
B.
1
2
,
1
2
√
,
1
3
C.
1
3
,
1
2
√
,
1
2
D.
1
2
,
1
2
√
,
1
2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
Let,
a
→
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
, then ,
Putting these values in (1) , we get :
# Vector Algebra
# CBSE 12th Mathematics
Prepare / Learn
Q10.
If
θ
θ
is the angle between two vectors
then
only when
A.
0<θ<π
B.
0<θ<π/2
C.
0⩽θ⩽π
D.
0⩽θ⩽π/2
View Solution
Add Work Space
Answer :
Option D
Explaination / Solution:
Submit My Answer
Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1 Mark for Wrong Answer : -0.5 Mark for Left Answer : 0
Save and Share My Score
REDO LAST TEST AGAIN : ( TEST 4 )
REDO THIS TEST AGAIN : ( TEST 5 )
START NEXT : ( TEST 6 )
Vector Algebra
| Online Objective Test |
Start Test
Under Graduate Entrance Exams : IIT JEE IEEE Entrance Exam (Mathematics)
| Online Objective Test
Start Test
UPSC Civil services Entrance exams : Civil Services Aptitude Test (CSAT) (Mathematics)
| Online Objective Test
Start Test
TANCET Anna University : EEE Electrical and Electronics Engineering (Mathematics)
| Online Objective Test
Start Test
TANCET Anna University : ECE Electronics and Communication Engineering (Mathematics)
| Online Objective Test
Start Test
TANCET Anna University : CSE, IT Computer Science Engineering and Information Technology (Mathematics)
| Online Objective Test
Start Test
TANCET Anna University : Civil Engineering (Mathematics)
| Online Objective Test
Start Test
TANCET Anna University : Mechanical Engineering (Mathematics)
| Online Objective Test
Start Test
Prepare Before Start Test
| Learn
Engineering
| prepare/Learn
Medical
| prepare/Learn
TN School (10th & 12th )
| prepare/Learn
NEET, JEE
| prepare/Learn
TNPSC Exam
| prepare/Learn
UPSC Civil services Entrance exams
| Online Test
General Studies test
| Start Online Test
Civil Services Aptitude Test (CSAT)
| Start Online Test
Interview and Personality Test
| Start Online Test
GATE Exam
| Online Test
EE Electrical Engineering
| Start Online Test
EC Electronics and Communication Engineering
| Start Online Test
CS Computer Science and Information Technology
| Start Online Test
CE Civil Engineering
| Start Online Test
ME Mechanical Engineering
| Start Online Test
Under Graduate Entrance Exams
| Online Test
IIT JEE IEEE Entrance Exam
| Start Online Test
NEET Entrance Exam
| Start Online Test
AIIMS Entrance Exams
| Start Online Test
Problem Solving and Reasoning
| Online Test
Verbal and Reading Comprehension
| Start Online Test
Data Interpretation and Logical Reasoning
| Start Online Test
Mathematics or Quantitative Aptitude
| Start Online Test
CAT Entrance Exams
| Online Test
Mathematics or Quantitative Aptitude
| Start Online Test
Data Interpretation and Logical Reasoning
| Start Online Test
Verbal and Reading Comprehension
| Start Online Test
CLAT LAW Entrance exams
| Online Test
English including comprehension
| Start Online Test
General Knowledge and Current Affairs
| Start Online Test
Elementary Mathematics
| Start Online Test
Logical and Legal Reasoning Aptitude
| Start Online Test
Banking Entrance exams
| Online Test
Bank PO
| Start Online Test
Bank Clerks
| Start Online Test
Specialist Officers (SO)
| Start Online Test
UGC NET Entrance exams
| Online Test
Science
| Start Online Test
Language
| Start Online Test
TANCET Anna University
| Online Test
EEE Electrical and Electronics Engineering
| Start Online Test
ECE Electronics and Communication Engineering
| Start Online Test
CSE, IT Computer Science Engineering and Information Technology
| Start Online Test
Civil Engineering
| Start Online Test
Mechanical Engineering
| Start Online Test
TN State Board
| Online Test
TN 11th Standard
| Start Online Test
TN 12th Standard
| Start Online Test
TN 10th Standard
| Start Online Test