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

## CBSE Class 12 Maths Chapter-10 Important Questions â€“ Free PDF Download

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 10 â€“ 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.

## 1 Mark Questions

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

2. Find the sum of the vectors.

Ans:Â

3. Find the direction ratios and the direction cosines of the vectorÂ
Ans:Â D.R ofÂ

D.C ofÂ

4. Find the angle between vectorsÂ
Ans:Â

5. VectorsÂ  be such thatÂ  thenÂ  is a unit vector. Find angle between .
Ans:Â

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

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

8. Find the direction ratios and the direction cosines of the vectorÂ
Ans:Â D.R ofÂ

9. FindÂ
Ans:

10. IfÂ
Ans:Â

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

13. Find the direction ratios and the direction cosines of the vectorÂ
Ans:Â D.R ofÂ

D.C ofÂ

14. Evaluate the productÂ
Ans:

15. FindÂ  ifÂ
Ans:Â

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

17. Compute the magnitude of
Ans:Â

18. Find the direction ratios and the direction cosines of the vectorÂ
Ans:Â D.R ofÂ

D.C ofÂ

19.Â  Is unit vector andÂ  Then findÂ
Ans:

20. Show thatÂ
Ans:Â

## 4 Mark Questions

1. Find the unit vector in the direction of the sum of the vectorsÂ
Ans:Â LetÂ

The required unit vector is

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

Hence, theÂ is a right angled triangle.

3. Show that the pointsÂ  are collinear.
Ans:Â

Hence points A, B, C are collinear.

4. IfÂ  are unit vector such thatÂ  find the value ofÂ
Ans:Â

5. IfÂ  are such thatÂ  is then find the value of .
Ans:Â

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:Â (i)Â

(ii)Â

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

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

8. Find a unit vectorÂ  to each of the vectorsÂ
Ans:Â A vector which isÂ to bothÂ is giving by

Req. unit vector is

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

Unit vector along

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

OBÂ¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯=2i^+3j^+4k^OBÂ¯=2i^+3j^+4k^
OCÂ¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯=i^+5j^+5k^OCÂ¯=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)

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

12. Find a vectorÂ  which isÂ  to bothÂ  andÂ  andÂ  . =15
LetÂ

Ans:

On solving equation (i) and (ii)

Put x, y, z in equation (iii)

13. LetÂ  be three vectors such thatÂ  and each one of them beingÂ  to the sum of the other two, findÂ
Ans:Â

14.Â IfÂ

Find the angel between the vectorsÂ
Ans:Â

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

Ans:Â

16. Three vectorsÂ  satisfy the conditionÂ  Evaluate the quantityÂ  ifÂ
Ans:Â

17. If with reference to the right handed system of mutuallyÂ  unit vectorsÂ  then expressÂ  in the form , whereÂ  is || toÂ  andÂ  is toÂ
Ans:Â

18. IfÂ  be three vectors such thatÂ  andÂ  find the angle betweenÂ
Ans:Â

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

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:Â