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Ncert Solutions for Class 12 Maths Three Dimensional Geometry Previous Exercises Exercise 11.1 Exercise 11.2 Exercixe 11.3 1. In each of the following cases ,determine the direction cosine of the nornal tothe plane and the distance from the origin .                       (a) \(z=2\)                                                 (b) x + y+z = 1                       (c) 2x + 3y - z = 5                                     (d) 5y +8 =0 Sol: (a) \(z=2\)  Dividing both sides of the equation by  \(\frac{1}{\sqrt{0^{2}+1^{2}+0^{2}}}\) = \(\frac{1}{\sqrt{1}}\) we get \(\dfrac{z}{\sqrt{1}}=\dfrac{2}{\sqrt{1}}\) z = 2 \(\th...

Question Paper for AHSEC English NCERT  2013 NCERT solutions for Class 12  English Flamingo   The Last Lesson The Roadside Stand Going Places The memoirs of the Chota Sahib A Thing of Beauty SECTION A (Reading Skills 10 Marks) 1.           Read the following passage carefully and answer the questions that follow: Inspite of all the honours that we heaped upon him, Pasteur, as has been said, remained     simple at heart. Perhaps the imagery of his boyhood days, when he drew the familiar scenes of his birthplace and the longing to be great artist, never wholly left him. IN truth he did become a great artist, though after his sixteenth year he abandoned the brush forever. Like every artist of worth, he put his whole soul and energy into his work, and it was this very energy that in the end wore him out. For him, each sufferer was something more than just a case that was to be cured. He ...

Class 12 Ncert Solutions English Flamingo A thing of Beauty A Thing of Beauty by John Keats Think it out 1. List the things of beauty mentioned in the poem. Ans: The poet John Keats has described a lot of things that are of beauty in the poem. According to him, a thing of beauty is something that gives us happiness which remains with us for good. It provides us liveliness and a sleep filled with pleasant dreams and never ceases to exist. He has mentioned the  sun, the moon, the old and young trees which gives shades to the simple sheep among such thing of beauty. Besides these, the daffodils living in the green world and the clear rills of water that serve as a "cooling covert" in the hot season for themselves are also included by the poet in the list of the things of beauty. Lastly, he mentioned the "mid forest brake " among which beautiful roses keep blooming providing a splendid view as a thing of beauty. 2. List the things that cause suffe...

Class 12 Ncert Solution Maths|| 3d Geometry                                      Class 12 Ncert Solution Maths|| 3d Geometry Previous Exercise Exercise 11.1 Next Exercise Exercise 11.3 Exercise 11.2 1. Show that the three lines with direction cosines \(\frac{12}{13}, \ \frac{-3}{13},\ \frac{-4}{13};\ \ \frac{4}{13},\ \frac{12}{13},\ \frac{3}{13};\ \ \frac{3}{13},\ \frac{-4}{13},\ \frac{12}{13}\) are mutually perpendicular. Sol: Two lines are perpendicular if the sum of the product of their direction cosines is equal to zero. If \(l_1,\ m_1,\ n_1\) and  \(l_2,\ m_2,\ n_2\) be the direction cosines of two lines then they are perpendicular if       \(l_1l_2 + m_1m_2 + n_1n_2=0\) \(\therefore\)\(l_1l_2 + m_1m_2 + n_1n_2\) =\(\frac{12}{13}.\frac{4}{13} + \frac{-3}{13}.\frac{12}{13} +\frac{-4}{13}.\frac{3}{13}\) = \(\frac{48}{169} - \fr...