** NCERT Solutions for Class 12 Maths Exercise 10.5 of Chapter 10 Vector Algebra: Miscellaneous Exercise**

NCERT Solutions for Class 12 Maths Exercise 10.5 of Chapter 10 Vector Algebra: Miscellaneous Exercise constitutes the summary of the whole chapter 10 of the class 12 maths NCERT textbook.Chapter 10 Vector Algebra: Miscellaneous Exercise is the most important for term 2 CBSE Board exam of class 12 maths because the miscellaneous exercise of vector algebra contains all types of the questions you have studied in exercise 10.1, exercise 10.2, exercise 10.3, and exercise 10.4.Here you can study class 12 maths NCERT solutions free of cost, therefore for any kind of update related to your study, you can subscribe us.

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**Q1.Write down a unit vector in the XY plane, making an angle of 30ยฐ with the positive direction of the ****x****-axis.**

Solution: Let us cosider asย a unit vector in XY-plane aking an angle ฮธ with the positive direction ofย *x*-axis

So,

Here ฮธย = **30ยฐ**

Hece the required unit vector isย ย

**Q2. Find the scalar components and magnitude of the vector joining the points P (x _{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}).**

Solution: The vector ย joining the points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) is

The magnitude of the vectorย is

Hence the scaler components are {(x_{2}– x_{1} ),(y_{2}– y_{1} ),(z_{2}– z_{1} )} and magnitude of is

**Q3. A girl walks 4 km towards the west, then she walks 3 km in a direction 30ยฐ east of the north and stops. Determine the girlโs displacement from her initial point of departure.**

Solution: Let the initial point of the girl is O, from Oย she walks 4 km towards the west up to the point P, then she walks 3 km in a direction 30ยฐ east of the north up to the point Q, it can be shown in the figure below.

As per the figure

Let’s find the displacement during the given journey,i.eย

According to the triangular rule of vector addition

**Hence, the the girlโs displacement from her initial point of departure is **

**Q4.Ifย ย ย ย ย ,then it is true thatย ย ?**

Solution: The given condition is

The given vectors can be drawn as in theย following figure

In ฮABC,

By the triangular rule of the addition of the vectors,we have

The magnitudes of the vectorsย ย represents the sides of the triangle

Since side of a triangle is always less than the sum of other two sides

Therefore it the given situation ย is not true.

**Q5.Find the value ofย x for whichย isย a unit vector.**

Solution:It is given to us that is a unit vector

ยฑxโ3 = 1

x = ยฑ1/โ3

**Q6.Find a vector of magnitude 5 units, and parallel to the resultant of the vectorsย **

Solution; The given vectors are

Let the resultant vector of the given vectors is

The unit vector in the direction ofย

Therefore the vector parallel to the resultant vectors of the magnitude 5 units

= ยฑ5รunit vector

Rationalizing denominator

**Q7.Ifย , find a unit vector parallel to the vectorย **

Solutions: The given vectors are

A unit vector parallel to the given vector is

Therefore unit vector parallel to the given vector is

**NCERT Solutions and CBSE notes for classes 9,10,11 and 12 of Maths and Science**

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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 |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

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Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

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**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 |

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