ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 24 (Vectors)

If θ be angle between u,v and u,v determine the sides of a triangle then the third side opposite to angle θ has length

• |u+v| A
• |u|+|v| B
• |u-v| C
• |u|-|v| D

• 1 A
• 0 B
• 
  C
• 
  D

• direction ratios A
• direction cosines B
• direction angles C
• none of these D

The ortho center of triangle whose vertices are (0,0)(3,0)(0,4) is

• (0,0) A
• (1,1) B
• (2,2) C
• (3,3) D

• [0, 0, 0] A
• [1, 0, 0] B
• [0, 1, 0] C
• [0, 0, 1] D

• [0, 0, 0] A
• [1, 0, 0] B
• [0, 1, 0] C
• [0, 0, 1] D

The unit vector along z-axis is

• 
  A
• 
  B
• 
  C
• none of these D

The position vector of a point (x, y) in xy plane is

• 
  A
• 
  B
• 
  C
• none of these D

• 0 A
• 90° B
• 180° C
• 360° D

Three points whose position vector a,b,c are collinear

• axb +b x c+ c x a = 0 A
• a,b +b,c +c,a =0 B
• a,|a xc| =0 C
• a+b+c =0 D

• 
  A
• 
  B
• 
  C
• 
  D

• a₁+ a₂ A
• a²₁+ a²₂ B
• 
  C
• 
  D

• 
  A
• 
  B
• 1 C
• 0 D

• [0, 0, 0] A
• [1, 0, 0] B
• [0, 1, 0] C
• [0, 0, 1] D

The magnitude of a vector can never be

• Zero A
• Negative B
• Positive C
• None of these D

3j . k x i

• 0 A
• 1 B
• 3 C
• 9 D

• 
  A
• 
  B
• 
  C
• 
  D

Projection of vector u along v is

• |v| cosθ A
• |u| cosθ B
• |v| sinθ C
• |u| sinθ D

Which of the following does not represent absolute value of a vector

• magnitude A
• length B
• norm C
• number D

• 
  A
• 
  B
• 
  C
• none of these D

Which of the following is not a unit vector

• [1, 1, 1] A
• [0, 1, 0] B
• [0, 0, 1] C
• [1, 0, 0] D

• Free vector A
• Null vector B
• Unit vector C
• None of these D

• perpendicular vectors A
• concurrent vectors B
• parallel vectors C
• none of these D

The direction cosines of y-axis are

• 1, 0, 0 A
• 0, 1, 0 B
• 0, 0, 1 C
• 1, 1, 1 D

• 
  A
• 
  B
• 
  C
• 
  D

If a,b,c are three non-coplanar vector then [a +b,b +c,c +a] = _____

• [a.b.c] A
• 2[a,b,c] B
• [abc]-2 C
• 2[abc]2 D

Which of the following is a scalar.

• electric field A
• magnetic field B
• weight C
• mass D

• 
  A
• 
  B
• 0 C
• 1 D

If a,b c are sides of a triangle taken in order then a x b =

• b x c A
• b x a B
• cxa C
• Both a & b D

If |a x b|2 + (a,b)2 = _____

• |a|2 + |b|2 A
• |a|2- |b|2 B
• |a|2|b|2 C
• None D