NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

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Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.3 is based on the topic Section Formula.

Download PDF NCERT Solutions for Class 12 Introduction to Three Dimensional Geometry Exercise 12.3

Check out the solutions of Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.3

Read More: NCERT Solutions For Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

Also check other Exercise Solutions of Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

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Chapter Related Topics
Angle Between Two Plane	Angle between two lines	Angle between line and plane

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CBSE CLASS XII Related Questions

1.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).
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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.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
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4.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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5.
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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6.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]
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