# 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.

## 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:

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

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16. Three vectors satisfy the condition Evaluate the quantity if
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17. If with reference to the right handed system of mutually unit vectors then express in the form, where is || to and isto
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18. If be three vectors such that and find the angle between
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19. Find the area of the ||gm whose adjacent sides are represented by the vectors,
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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: