All questions of Vector Algebra for JEE 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)
  Trapezium
• b)
  Rectangle
• c)
  Square
• d)
  Parallelogram

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

• a)
  
• b)
  
• c)
  
• d)
  

The value of  is:

• a)
  0
• b)
  3
• c)
  1/3
• d)
  1

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

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

• a)
  
• b)
  
• c)
  
• d)
  

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

• a)
  4
• b)
  7
• c)
  5
• d)
  ± 6

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)
  

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

In the triangle ABC, which statement is not true?

• a)
  
• b)
  
• c)
  
• d)
  

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

Let α, β, γ be distinct real numbers. The points with position vectors 

• a)
  are collinear
• b)
  form an equilateral triangle
• c)
  form a scalene triangle
• d)
  form a right angled triangle

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

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

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

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

The projection of the vector  on the vector is:​

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

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

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

• a)
  
• b)
  
• c)
  
• d)
  

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

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

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

• a)
  
• b)
  
• c)
  
• d)
  

The angle between the vectors is:    is :

• a)
  
• b)
  
• c)
  
• d)
  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

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)
  

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

• a)
  
• b)
  
• c)
  
• d)
  

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

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 number of distinct real values of λ, for which the vectors  are coplanar, is

• a)
  zero
• b)
  one
• c)
  two
• d)
  three

If a be magnitude of vector  then​

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

If  , then   ........

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

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

Let   be three non - coplanar vectors and   are vectors defined by the relations   then the value of the expression   is equal to

• a)
  0
• b)
  1
• c)
  2
• d)
  3.

• a)
  a = –40
• b)
  a = 40
• c)
  a = 20
• d)
  none of these

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

Let be three vector s. A vector the plane of   whose projection on  , is given by 

• a)
  
• b)
  
• c)
  
• d)
  

The value of k such that  lies in the plane 2x – 4y + z = 7, is

• a)
  7
• b)
  –7
• c)
  no real value
• d)
  4

• 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

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

• 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

If  , then

• a)
  
• b)
  
• c)
  
• d)
  

The volume of the parallelopiped whose sides are given by 

• a)
  4/13
• b)
  4
• c)
  2/7
• d)
  none of these

Let  be unit vectors such that  Which one of the following is correct ?

• a)
  
• b)
  
• c)
  
• d)
   are muturally perpendicular

• a)
  1
• b)
  √2
• c)
  √3
• d)
  2

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

If   are unit vectors, then  does NOT exceed

• a)
  4
• b)
  9
• c)
  8
• d)
  6