1.Represent graphically a  displacement of 40 km, 30^o East of North. 

  
Here, vector   represents the displacement of 40 km, 30^o East of North.  

2. Write the magnitude of  

Let 

3.  Find the scalar and vector components of the vector with initial point (2,1) and terminal point ( -5, 7 )

The vector with the initial point  P ( 2,1 )   and  terminal point Q  ( -5, 7 ) can be given by 
                     
Hence the required scalar components are -7  and 6 and the vector components are  

Q4. Find the sum of the vectors 

The given vectors are 
 

5. Find the unit vector in the direction of the vector 

6. Find the position vector of the midpoint of the vector joining the points P (2, 3, 4 )  and Q ( 4, 1, -2 ).

The position vector of mid - point R of the vector  joining points  P ( 2, 3, 4 ) and Q ( 4, 1, -2 )  is given by 
 

7. Show that the points A, B  and C  with position vectors,  respectively form the vertices  of a right angled triangle.

Position vectors of points A, B and  C  are  respectively given as 
 

8. Find the angle between the vectors  

The given vectors are 
                  

9. Find the projection of the vector 

10.

11.  If the vertices A,B,C of a  ΔABC  are ( 1, 2, 3 ),  ( -1, 0,0), ( 0,1,2 )  respectively.  then find  ∠ABC. [ ∠ABC is the angle between the vectors 

The vertices of  ΔABC are given as  A (1, 2, 3 ), B ( -1, 0, 0 )  and C ( 0,1,2 ).
Also it is given that  ∠ ABC  is the angle between the  vectors  
              

12. 

13. Find λ and μ  if   

14. Find the area of the triangle ABC with vertices  A (1, 1, 2 ),    B  ( 2, 3, 5 )  and  C ( 1, 5, 5 ).
 The vertices of Δ ABC are given as  A (1, 1, 2 ),    B  ( 2, 3, 5 )  and  C ( 1, 5, 8 )
The adjacent sides   
                              
 

15. Find the area of parallelogram whose adjacent  sides are determined by the vector 

Adjacent sides are given as