Vector Addition And Vector Subtraction - Practice Questions & MCQ

• For the simple case in which both vectors have the same direction

1. Vector addition-

•  Vectors quantities are not added to simple algebraic rules, because of their direction that matter.

• Addition of vector means determining their resultant.

• When two vectors are in the same direction then upon addition the direction of the resultant vector is the same as any of the two vectors, while the magnitude of the resultant vector is simply the algebraic sum of two vectors.

• eg, Vector has magnitude 4 & vector has magnitude  2 in same direction. 

                     So resultant has magnitude equal to 6 while its direction is either along or

     2) Vector Subtraction-

• Vector subtraction of from is equal to Vector addition of and negative vector of .

• eg,Vector and are in east direction with  magnitudes 4 and 2 respectively.  

            Vector subtraction of from is equal

              Resultant vector has magnitude 2  in east direction.

• For the  case when both vectors does not have the same direction

1. Triangle law of vector Addition

  If two vectors are represented by both magnitude and direction by two sides of triangle taken in same order then their resultant is represented by side of triangle. 

Figure represents triangle law of vector Addition

So resultant  side C is given by 

Where = angle between two vectors.

2.  Parallelogram law of vector Addition 

• If two vectors are represented by both magnitude and direction by two adjacent side of parallelogram taken from same point then their resultant is also represented by both magnitude and direction taken from the same point but by diagonal  of parallelogram.

• 

 Figure represents  law of parallelogram vector Addition

• Commutative law-

Sum of vector remains the same in whatever order they may be added.

Fig. Shows Commutative law of vector addition.