NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3 is covered in this article with a detailed explanation. Chapter 10 Vector Algebra Exercise 10.1 covers basic concepts of the product of two vectors, multiplication of vector by a scalar, and projection of a vector on a line.

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Check out other exercise solutions of Class 12 Maths Chapter 10 Vector Algebra

Class 12 Chapter 10 Vector Algebra Topics:

Properties of scalar product of two vectors	Laws of Vector Addition	Vector Formula
Magnitude of a vector	Vector Projection Formula	Scalar triple product of vectors
Direction of a vector	Adjacency Matrix	Components of vector
Vector Space	Cross product	Vector Calculus

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Math Formula	Difference between in Maths
Math MCQs	Math Study Notes	Calculus
Mensuration	Arithmetic	Trigonometry

CBSE CLASS XII Related Questions

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

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2.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

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4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

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5.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

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6.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3

CBSE CLASS XII Related Questions

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

2.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

5.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3

CBSE CLASS XII Related Questions

1.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

2.Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

3.Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

4.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

5.Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

2.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

3.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

5.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]