**NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra**

NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra will help you to boost your maths preparation for the term 2 CBSE Board exam 2021-22. All the unsolved questions of the exercise 10.2 of chapter 10-Vector Algebra are solved by an expert of maths as per the CBSE norms, NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra is the most important input study material for the preparation of CBSE Board exam, engineering entrance exams, NDA, CBSE, and other UPSE entrance exams. You can study here all the study material free of the cost and download free PDFs.

**NCERT solutions for class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

**Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2**

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**NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra**

**Q1. Compute the magnitude of the following vectors:**

Ans. Given vectors are

**Q2. Write two different vectors having same magnitude.**

Solution: Two vectors with the same magnitude are supposed be different when their directions are different.

Let one of the vector isย ย

Then another vector that is equal to this vector but has a different direction is given by

Both of vector are different but equal in magnitude

**Q3. Write two different vectors having same direction.**

Solution: Let one of the vector is given by

Then another vector that has the same direction is given by

Direction cosines of vector ย are l,m, and n are given by

Direction cosines of vector ย are l,m, and n are given by

Both of the vectors have the same direction because both have the same direction cosines.

**Q4. Find the values ofย ****x****ย and****ย y****ย so that the vectors**** ย andย ย are equal.**

Solution: It is given that

If both vectors and are equal, then their components should be equal

Therefore x = 2 and y =3

**Q5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (โ5, 7).**

Solution:

Let the given initial point is named P(2,1) and Q(-5,7)

Then the vectorย is given by

Hence scaler component of the vector , are -7 and 6 while vector components areย andย .

**Q6. Find the sum ofย the vectors**

Solutions: The given vectors are

Q7.Find the unit vector in the direction of the vector.

Solution:The unit vector ( )in the direction of the vectorย ย is given by

**Q8. Find the unit vector in the direction of the vector, where P and Q are the points ****(1, 2, 3) and (4, 5, 6), respectively.**

Solution: The given points are P(1, 2, 3) and Q(4, 5, 6)

The vector passing through the given points is given as

The unit vector in the direction ofย ย ย is given as

**Q9.For given vectors, ****and****, ย find the unit vector in the direction of the vectorย **

Solution:

The given vectors areย ** ย ****and****,ย **

The vector ย is the sum of the given vectors

The unit vector in the direction ofย the vectorย ย is given as

**Q10. Find a vector in the direction of vectorย **** which has magnitude 8 units.**

Solution: The unit vector in the direction ofย the given vectorย is given as

Since theย vector we have to determine is of the magnitude of 8

Therefore the vector in the direction of vectorย ย is

**Q11. Show that the vectors ย andย ย are****ย collinear.**

Solutions: Two vectors are collinear when

Where ฮป is a scaler

Let the given vectors are

Where ฮป = -2

Therefore both vectors are collinear

**Q12. Find the direction cosines of the vectorย **** .**

Solution: The direction cosines (l,m,n)of the given vector are given by

**Q13. Find the direction cosines of the vector joining the points A (1, 2, โ3) andย ****B (โ1, โ2, 1) directed from A to B.**

Solutions:

The given points are A (1, 2, โ3) andย B (โ1, โ2, 1)

Direction cosines (l,m,n) of the vector ย are

**Q14. Show that the vectorย ย ****is equally inclined to the axes OX, OY, and OZ.**

Solution: The given vector isย ย

The direction cosines(l,m,n) are

Let the angles made by the given vector with OX, OY, and OZ areย ฮฑ, ฮฒ and ฮณ,since we have got l=cosฮฑ, m = cosฮฒ, n = cosฮณ

It is clear that the given vector is equally inclined to the axes OX, OY, and OZ.

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**NCERT Solutions for class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

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