Important Questions for CBSE Class 12 Maths Chapter 10 – Vector Algebra

CBSE Class 12 Maths Chapter-10 Important Questions – Free PDF Download

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 10 – Vector Algebra prepared by expert Maths teachers from latest edition of CBSE(NCERT) books, On CoolGyan.Org to score more marks in CBSE board examination.
You can also Download Maths Revision Notes Class 12 to help you to revise complete Syllabus and score more marks in your examinations.
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CBSE Class 12 Mathematics Important Questions Chapter 10 – Vector Algebra


1 Mark Questions

1. Is the measure of 5 seconds is scalar or vector?
Ans: Scalar


2. Find the sum of the vectors.

Ans: 


3. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 

D.C of 


4. Find the angle between vectors 
Ans: 


5. Vectors  be such that  then  is a unit vector. Find angle between .
Ans: 



6. Is the measure of 10 Newton is scalar or vector.
Ans:Vector


7. Write two different vectors having same magnitude.
Ans: 



8. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 


9. Find 
Ans:




10. If 
Ans: 





11. Is the measure of 20 m/s towards north is scalar or vector.
Ans: Vector
12. 
Ans: 


13. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 

D.C of 


14. Evaluate the product 
Ans:


15. Find  if 
Ans: 


16. Is the measure of 30 m/s towards north is scalar or vector.
Ans: Scalar


17. Compute the magnitude of
Ans: 


18. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 

D.C of 


19.  Is unit vector and  Then find 
Ans:



20. Show that 
Ans: 




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4 Mark Questions

1. Find the unit vector in the direction of the sum of the vectors 
Ans: Let 



The required unit vector is



2. Show that the points  are the vertices of right angled triangle.
Ans: 




Hence, the is a right angled triangle.


3. Show that the points  are collinear.
Ans: 





Hence points A, B, C are collinear.


4. If  are unit vector such that  find the value of 
Ans: 








5. If  are such that  is then find the value of .
Ans: 






6. Consider two point P and Q with position vectors . Find the positions vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally (ii) externally.
Ans: (i) 

(ii) 


7. Show that the points A, B, C with position vectors  respectively are collinear.
Ans: 






Thus but one point B is common to both vectors hence A, B, C are collinear.


8. Find a unit vector  to each of the vectors 
Ans: A vector which is to both is giving by





Req. unit vector is


9. The scalar product of the vector  with a unit vector along the sum of vectors  is equal the one. Find the value of 
Ans: 


Unit vector along









10. Find the area of the  with vertices A (1, 1, 2) B (2, 3, 4) and C (1, 5, 5).
Ans: A (1, 1, 2) B(2, 3, 4) C (1, 5, 5)

OB¯¯¯¯¯¯¯¯=2i^+3j^+4k^OB¯=2i^+3j^+4k^
OC¯¯¯¯¯¯¯¯=i^+5j^+5k^OC¯=i^+5j^+5k^






11. Show that the points A (1, -2, -8) B (5, 0, -2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
Ans:A (1, -2, -8), B (5, 0, -2), C (11, 3, 7)








Thus and one point B is common there fore A, B, C are collinear and B divides AC in 2:3.


12. Find a vector  which is  to both  and  and  . =15
Let 



Ans:







On solving equation (i) and (ii)



Put x, y, z in equation (iii)






13. Let  be three vectors such that  and each one of them being  to the sum of the other two, find 
Ans: 




14. If 

Find the angel between the vectors 
Ans: 








15. Find the sine of the angel between the vectors.


Ans: 




16. Three vectors  satisfy the condition  Evaluate the quantity  if 
Ans: 




Adding (i) (ii) and (iii)


17. If with reference to the right handed system of mutually  unit vectors  then express  in the form , where  is || to  and  is to 
Ans: 






18. If  be three vectors such that  and  find the angle between 
Ans: 






19. Find the area of the ||gm whose adjacent sides are represented by the vectors, 
Ans: 



20. Find the vector joining the points P (2, 3, 0) and Q (-1, -2, -4) directed from P to Q. Also find direction ratio and direction cosine.
Ans: 

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