NCERT Solutions for Class 12 Maths Exercise 10.5 of Chapter 10 Vector Algebra: Miscellaneous Exercise - Future Study Point

# 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 (x1, y1, z1) and Q (x2, y2, z2).

Solution: The vector ย  joining the points P (x1, y1, z1) and Q (x2, y2, z2) is

The magnitude of the vectorย  is

Hence the scaler components are {(x2– x1 ),(y2– y1 ),(z2– z1 )} 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 girlโs 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 girlโs 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 ฮABC,

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

ยฑxโ3 = 1

x = ยฑ1/โ3

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

= ยฑ5รunit 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

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## NCERT Solutions of Science and Maths for Class 9,10,11 and 12

### NCERT Solutions for class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions for class 9 scienceย

 Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion Chapter 2-Is matter around us pure? Chapter 10- Gravitation Chapter3- Atoms and Molecules Chapter 11- Work and Energy Chapter 4-Structure of the Atom Chapter 12- Sound Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ? Chapter 6- Tissues Chapter 14- Natural Resources Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources Chapter 8- Motion Last years question papers & sample papers

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### NCERT Solutions for class 10 maths

 Chapter 1-Real number Chapter 9-Some application of Trigonometry Chapter 2-Polynomial Chapter 10-Circles Chapter 3-Linear equations Chapter 11- Construction Chapter 4- Quadratic equations Chapter 12-Area related to circle Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume Chapter 6-Triangle Chapter 14-Statistics Chapter 7- Co-ordinate geometry Chapter 15-Probability Chapter 8-Trigonometry

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 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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