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 30° with the positive direction of the x-axis.
Solution: Let us cosider as a unit vector in XY-plane aking an angle θ with the positive direction of x-axis
So,
Here θ = 30°
Hece the required unit vector is
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 joining the points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) is
The magnitude of the vector 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 30° east of the north and stops. Determine the girl’s displacement from her initial point of departure.
Solution: Let the initial point of the girl is O, from O she walks 4 km towards the west up to the point P, then she walks 3 km in a direction 30° 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.e
According to the triangular rule of vector addition
Hence, the the girl’s displacement from her initial point of departure is
Q4.If ,then it is true that ?
Solution: The given condition is
The given vectors can be drawn as in the following figure
In ΔABC,
By the triangular rule of the addition of the vectors,we have
The magnitudes of the vectors 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 is not true.
Q5.Find the value of x for which is a unit vector.
Solution:It is given to us that is a unit vector
±x√3 = 1
x = ±1/√3
Q6.Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
Solution; The given vectors are
Let the resultant vector of the given vectors is
The unit vector in the direction of
Therefore the vector parallel to the resultant vectors of the magnitude 5 units
= ±5×unit vector
Rationalizing denominator
Q7.If , find a unit vector parallel to the vector
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 3- Trigonometry | Chapter 11-Conic Sections |
Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |
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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 |
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Chapter 7- Integrals | |
Chapter 8-Application of Integrals |
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