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

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**CBSE Class 12 Mathematics Important Questions Chapter 10 â€“ Vector Algebra**

**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

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**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

Adding (i) (ii) and (iii)

**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