All questions of Vectors Algebra for Commerce Exam

The area of triangle whose adjacent sides are is :

• a)
  √70/2 sq. units
• b)
  9√2 /2 sq. units
• c)
  3√3 /2 sq. units
• d)
  2√3 /2 sq. units

A vector of magnitude 14 units, which is parallel to the vector

• a)
  
• b)
  
• c)
  
• d)
  

• a)
  Trapezium
• b)
  Rectangle
• c)
  Square
• d)
  Parallelogram

If  and , then the value of scalars x and y are:

• a)
  x = 1 and y = -2
• b)
  x = -2 and y = 1
• c)
  x = 2 and y = -1
• d)
  x = 2 and y = 1

• a)
  3b – 2a
• b)
  3a – b
• c)
  3a – 2b
• d)
  3b – a

• a)
  
• b)
  
• c)
  
• d)
  

The unit vector in the direction of , where A and B are the points (2, – 3, 7) and (1, 3, – 4) is:

• a)
  
• b)
  
• c)
  
• d)
  

In the triangle ABC, which statement is not true?

• a)
  
• b)
  
• c)
  
• d)
  

The points with position vectors  are collinear vectors, Value of a =​

• a)
  -20
• b)
  20
• c)
  -40
• d)
  40

The value of  is:

• a)
  0
• b)
  3
• c)
  1/3
• d)
  1

If | a | = 2, | b | = 5 and | a × b | = 8, thencan be equal to

• a)
  4
• b)
  7
• c)
  5
• d)
  ± 6

• a)
  zero vector
• b)
  Negative of the vector
• c)
  unit vector
• d)
  The vector itself

• a)
  |a – b| ≥ |a| – |b|
• b)
  |a + b| ≤ |a| + |b|
• c)
  |a + b| ≤ |a| – |b|
• d)
  |a – b| = |a + b|

If  are unit vectors along X-axis, Y-axis and Z-axis respectively, then

• a)
  
• b)
  
• c)
  
• d)
  

The projection of the vector  on the vector is:​

• a)
  10/ √6
• b)
  10/ √17
• c)
  2
• d)
  None of the above

• a)
  (-1,3)
• b)
  (1,-3)
• c)
  (1,3)
• d)
  (-1,-3)

If  are two vectors, such that , then = ……​

• a)
  3
• b)
  √7
• c)
  √5
• d)
  √3

The angles α, β, γ made by the vector with the positive directions of X, Y and Z-axes respectively, then the direction cosines of the vector are: 

• a)
  cos α, cos β, cos γ
• b)
  sin α, sin β, sin γ
• c)
  180° - α, 180° - β, 180° γ
• d)
  tan α, tan β, tan γ

If the magnitude of the position vector is 7, the value of x is:​

• a)
  ±1
• b)
  ±5
• c)
  ±3
• d)
  ±2

If a be magnitude of vector  then​

• a)
  a > 0
• b)
  a ≤ 0
• c)
  a ≥ 0
• d)
  a < 0

• a)
  Two or more vectors having the same final point
• b)
  Two or more pseudo vectors having the same initial point
• c)
  Two or more force vectors having the same initial point
• d)
  Two or more vectors having the same initial point

• a)
  zero vector
• b)
  unit vector
• c)
  equal vectors
• d)
  coterminus vectors

If a unit vector  makes angles and an acute angle θ with , then the components of  are

• a)
  
• b)
  
• c)
  
• d)
  

• a)
  
• b)
  
• c)
  
• d)
  

• a)
  √26 units
• b)
  5 units
• c)
  √20 units
• d)
  4 units

If  are position vectors of the points (- 1, 1) and (m, – 2). then for what value of m, the vectors  are collinear. 

• a)
  1
• b)
  2
• c)
  -1
• d)
  -2

The angle between the vectors is:    is :

• a)
  
• b)
  
• c)
  
• d)
  0

If  , then

• a)
  
• b)
  
• c)
  
• d)
  

The position vectors of the end points of diameter of a circle are   and  , then the position vector of the centre of the circle is:

• a)
  
• b)
  
• c)
  
• d)
  

If   are any two vectors, then

• a)
  
• b)
  
• c)
  
• d)
  

For what values of x and y, the vectorsare equal?

• a)
  
• b)
  x = 3, y = 6
• c)
  
• d)
  x = 6, y = 3

If  , then   ........

• a)
  √58
• b)
  √51
• c)
  √41
• d)
  4√3

• a)
  Is towards the origin
• b)
  Is towards a fixed point
• c)
  Does not exist
• d)
  Is indeterminate

Direction: Read the following text and answer the following questions on the basis of the same:

Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.

A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P₁(6, 8, 4), P₂(21, 8, 4), P₃(21, 16, 10) and P₄(6, 16, 10)

Q. What is the magnitude of and in what units?

• a)
  100
• b)
  150
• c)
  50
• d)
  90

• a)
  if they are in the same line
• b)
  if they are have equal magnitude
• c)
  if the direction cosines of one are negatives of the other
• d)
  if they are parallel to the same lineirrespective of their magnitudes and directions.

• a)
  केवल 1
• b)
  केवल 2
• c)
  दोनों 1 और 2
• d)
  इनमे से कोई भी नहीं

• a)
  Perpendicular to each other and have the original vector as their resultant 
• b)
  Parallel to each other and have the original vector as their resultant 
• c)
  Arbitrary vectors which have original vectors as their resultant 
• d)
  It is impossible to resolve a vector

• a)
  A vector whose direction angle γ is unity
• b)
  A vector whose magnitude is unity
• c)
  A vector whose direction angle α is unity
• d)
  A vector whose direction angle β is unity

Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as

Assertion (A): The area of parallelogram with diagonals

Reason (R): If represent the adjacent sides of a triangle, then the area of triangle can be obtained by evaluating

• a)
  Both A and R are true and R is the correct explanation of A
• b)
  Both A and R are true but R is NOT the correct explanation of A
• c)
  A is true but R is false
• d)
  A is false but R is True

• a)
  2 :1
• b)
  3 :2
• c)
  2 :4
• d)
  2 : 3

• a)
  केवल 1 और 2
• b)
  केवल 3
• c)
  2 और 3 ही
• d)
  1 ही

• a)
  terminal point, end point.
• b)
  initial point, terminal point
• c)
  Origin, end point
• d)
  initial point, end point

Direction: Read the following text and answer the following questions on the basis of the same:

A class XII student appearing for a competitive examination was asked to attempt the following questions.

Let be three non zero vectors.

Q. are unit vectors and θ be the angle between them then

• a)
  sin θ/2
• b)
  2sin θ/2
• c)
  2cos θ/2
• d)
  cos θ/2

Direction: Read the following text and answer the following questions on the basis of the same:

ABCD is a parallelogram whose adjacent sides are represented by the vectors Three of its vertices are A(1, 2, 3), B(2, 0, 5) and D(–1, 4, 1).

Q. The diagonal

• a)
  
• b)
  
• c)
  
• d)
  

• A:

  lr, mr and nr

• B:

  lr, m and nr

• C:

  l, mr and nr

• D:

  lr, mr and n 

The answer is a.

• a)
  co-terminus vectors.
• b)
  zero vectors
• c)
  co-initial vectors
• d)
  unit vectors

• a)
  are cosines of Direction angles
• b)
  arecotangents of Direction angles
• c)
  are tangents of Direction angles
• d)
  aresines of Direction angles

• a)
  45
• b)
  20
• c)
  48.5
• d)
  25√2

• a)
  
• b)
  
• c)
  
• d)
  

 are any three vectors then the correct expression for distributivity of scalar product over addition is

• a)
  
• b)
  
• c)
  
• d)