1. If the position vector of point (12, n) is (13, 0, 0), then n = 13. 2. The document contains vector questions related to finding unit vectors, angles between vectors, dot products, volumes of parallelepipeds, collinearity and coplanarity of points. 3. Questions involve calculations of vector components, magnitudes, directions and relationships between multiple vectors.

1. Vector Questions (Cont…)
1
1. If the p.v. a of a point (12, n) is such that a 13 , find the value of ‘n’.
2. Find a unit vector parallel to the vector (a)  3i 4j   (b)  i 2j 
3. Find a unit vector in the direction of a 3i 2j k.    
4. Find a unit vector in the direction of a i 2j k    that has magnitude of 5 units.
5. Find a unit vector in the direction of AB , where    A 2,1,4 and B 1,1,3  .
6. a, b ,c be the vectors represented by the sides of a ABC , taken in order, then prove that a b c 0   .
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7. Find the angle between two vectors a and b

with magnitude 2 and 1 respectively and such that a b 3


8. Let a 4i 5j k, b i 4j 5k and c 3i j k        
          . Find a vector d

which is perpendicular to both a and b

and
satisfying d c 21.
 

9. Dot products of a vector with vectors ˆ ˆ ˆ(3i 5k),(2i 7j) and (i j k)       are respectively 1,6,5 . Find the vector.
10. Find ˆ ˆ ˆx ,if for a unit vector a, (x a) (x a) 15.  
  

11. Find a and b if, (a b) (a b) 27 and a 2 b   
      

12. If a b 60; a b 40 and b 40, find a    
    
.
13. Show that the vector (i j k)    is equally inclined with the coordinate axes.
14. Find a unit vector perpendicular to both the vectors (i 2j 3k) and (i j 2k)         .
15. Find a unit vector perpendicular to both the vectors   a b and a b 
  
where a 3i j and b i j 2k    
     .
16. If 2 5 8a , b and a b , find a b.   
    

17. If 13 5 60   a , b and a b , find a b .
    

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18. Find the volume of a parallelepiped whose sides are
(a) ˆ ˆ ˆ ˆ(2i 7j),(2i 5j 6k) and ( i 2j k)         (b) ˆ ˆ ˆ ˆ(2i 7j 6k),(i j k) and (i 2j k)         
19. Show that the following vectors are coplanar
(a) ˆ ˆ ˆ ˆ( 2i 2j 4k),( 2i 4j 2k) and (4i 2j 2k)            (b) ˆ ˆ ˆ ˆ(i 2j k),(3i 2j 7k) and (5i 6j 5k)         
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20. Prove that the following points are collinear.
(i) 6, 7, 1 , 2, 3,1 4, 5,0 (ii) 2, 1, 3 , 4, 3,1 3, 1, 2
21. Prove that the following points are coplanar.
(i) 6, 7, 0 , 16, 19, 4 , 0, 3, 6 2, 5, 10 (ii) 2, 3, 1 , 1, 2,3 , 3, 4, 2 1, 6, 6