A level Vector Algebra Quiz 1

15 Questions

Quiz Description

Hello, and welcome to this amazing quiz. Here, we will be looking at vector algebra and its applications. I guess we all know what vectors are right? Right away, we will move on by looking at vector arithmetic (addition, subtraction, multiplication), equations of a line, equations of a plane, the areas and volumes of solid figures, etc. It is going to be an exciting experience learning and applying what you have studied on vectors.

A vector quantity is a physical quantity that has both magnitude and direction. An example of a vector is a force. In mathematics, vectors are usually represented by a directed line with a value sometimes attached to it. This value represents the magnitude, and the arrow on the line represents the direction. In this light, we can say that vector algebra is an algebra for which the elements involved may likely represent vectors and the postulations and rules are based on the behavior of vectors. Just like in normal algebra, we can also perform arithmetic operations on vectors such as addition, subtraction, and multiplication. One very good advantage of vector algebra is that it is easier to apply as compared to geometry, and it requires the knowledge of fewer rules.

Are you a fan of mathematics? Then you are in the right place. Practice with us by going through the various mathematics quizzes available here. Happy solving. 

1:

The area of parallelogram whose adjacent sides are i−2j +3k and 2i+j−4k is


Correct
  • 1:
    10√6
  • 2:
    5√6
  • 3:
    10√3
  • 4:
    5√3
2:

If AB × AC = 2i − 4j + 4k, then the are of ΔABC is


Correct
  • 1:
    3 sq. units
  • 2:
    4 sq. units
  • 3:
    16 sq. units
  • 4:
    9 sq. units
3:

|a × b|^2 + |a.b|^2 = 144 and |a| = 4, then |b| is equal to


Correct
  • 1:
    12
  • 2:
    3
  • 3:
    8
  • 4:
    4
4:

If |a × b| = 4 and |a.b| = 2, then |a|^2 |b|^2 is equal to


Correct
  • 1:
    2
  • 2:
    6
  • 3:
    8
  • 4:
    20
5:

If |a|= 5, |b|= 13 and |a × b|= 25, find a.b


Correct
  • 1:
    ±10
  • 2:
    ±40
  • 3:
    ±60
  • 4:
    ±25
6:

Find the value of λ so that the vectors 2i−4j+k and 4i−8j+λk are parallel


Correct
  • 1:
    -1
  • 2:
    3
  • 3:
    -4
  • 4:
    2
7:

If O is origin and C is the mid point of A(2, -1) and B(-4, 3), then the value of OC is


Correct
  • 1:
    i + j
  • 2:
    i − j
  • 3:
    −i + j
  • 4:
    −i − j
8:

The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is


Correct
  • 1:
    √3
  • 2:
    1 – √3
  • 3:
    1 + √3
  • 4:
    -√3
9:

The value of λ for which the vectors 3i − 6j + k and 2i − 4j + λk are parallel is


Correct
  • 1:
    2/3
  • 2:
    3/2
  • 3:
    5/2
  • 4:
    2/5
10:

The vectors from origin to the points A and B are a = 2i − 3j + 2k and b = 2i + 3j + k, respectively then the area of triangle OAB is


Correct
  • 1:
    340
  • 2:
    √25
  • 3:
    √229
  • 4:
    (1/2) √229
11:

The vectors λi + j + 2k, i + λj − k and 2i − j + λk are coplanar if


Correct
  • 1:
    λ = -2
  • 2:
    λ = 0
  • 3:
    λ = 1
  • 4:
    λ = -1
12:

If a, b, c are unit vectors such that a + b + c = 0, then the value of a.b + b.c + c.a is


Correct
  • 1:
    1
  • 2:
    3
  • 3:
    −3/2
  • 4:
    None of these
13:

If |a| = 4 and -3 ≤ λ ≤ 2, then the range of |λa| is


Correct
  • 1:
    [0, 8]
  • 2:
    [-12, 8]
  • 3:
    [0, 12]
  • 4:
    [8, 12]
14:

The number of vectors of unit length perpendicular to the vectors a = 2i + j + 2k and b = j + k is


Correct
  • 1:
    one
  • 2:
    two
  • 3:
    three
  • 4:
    infinite
15:

Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a.b + b.c + c.a is


Correct
  • 1:
    47
  • 2:
    25
  • 3:
    50
  • 4:
    -25

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A level Vector Algebra Quiz 1
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