Page 1 - XII-CH10-VECTOR-Work Sheets

XII:CH – 10.VECTOR
WORK SHEET

Answer the following:-
           
  
1. If a b c d and a c b d show that (a d ) is parallel to (b c ) , it is being given
  
   
that a d and b c .
   
2. Express the vector a 5i 2 j 5k   as the sum of two vectors such that one is parallel to
   
the vector b 3i k  and the other is perpendicular to b .
3. Using vectors find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and
C (1, 5, 5)
     




4. The two adjacent sides of a parallelogram are 2i 4 j 5k and i 2 j 3k . Find the unit
vector parallel to one of its diagonals. Also find its area.
            
5. Let a   4 j 2k , b 3i 2 j 7k   and c 2i j 4k   . Find a vector p which is

i
   

perpendicular to both a and b and p.c 18 .
           



6. If a    , b 4 i 2 j 3k and c   
i j k
i 2 j k , find a vector of magnitude 6 units
  


which is parallel to the vector 2a b 3c .
7. Find the value of  such that the following vectors are coplanar:
           
i j k,b 2i j k, c   
a       i j  .
k
̂
8. Show that four points whose position vectors are 4 + 8 ̂ + 12 , 2 + 4 ̂ + 6 , 5
̂
̂
̂
̂
̂
̂
̂
3 + 5 ̂ + 4 and 5 + 8 ̂ + 5 are coplanar.
  


9. The scalar product of the vector i j k with the unit vector along the sum of vectors
     


 

2i 4 j 5k and i 2 j 3k is equal to one. Find the value of .
        



 
10. If a ,b , c are three vectors such that |a| 5,|b| 12and|c| 13 and a b c  , then
0
     


find the value of a.b b.c c.a .

11. Find the scalar components of the vector AB with initial point A (2, 1) and terminal
point B (– 5, 7).
  
12. Write the direction cosines of the vector 2i j 5k   .
⃗⃗
⃗⃗
⃗⃗
13. | | = 4 , | | = 3 . = 6√3, ℎ ℎ | × |.
⃗
⃗
⃗
14. Find the position vector of the point which divides the join of points with position
⃗⃗
⃗⃗
⃗
⃗
vectors + 3 and − internally in the ratio 1:3.