Here you will learn section formula in 3d for both internal and external division with examples. For distance formula and section formula in 2d for internal and external division see this What is the Section Formula | Distance Formula in 2d. Let’s begin – Section Formula in 3d (a) Internal Division Let P\((x_1, y_1, z_1)\) […]
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Here you will learn distance formula in 3d to calculate distance between two points with example. Let’s begin – Distance Formula in 3d The distance between the points P\((x_1, y_1, z_1)\) and Q\((x_2, y_2, z_2)\) is given by PQ = \(\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2}\) Proof : Let O
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Here you will learn some trigonometry examples for better understanding of trigonometry concepts. Example 1 : \(sin5x + sin2x – sinx\over {cos5x + 2cos3x + 2cos^x + cosx}\) is equal to – Solution : L.H.S. = \(2sin2xcos3x + sin2x\over{2cos3x.cos2x + 2cos3x + 2cos^2x}\) = \(sin2x[2cos3x+1]\over {2[cos3x(cos2x+1)+(cos^2x)]}\) = \(sin2x[2cos3x+1]\over {2[cos3x(2cos^2x)+(cos^2x)]}\) = \(sin2x[2cos3x+1]\over {2cos^2x(2cos3x+1)}\) = tanx Example
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Here you will learn some trigonometric equation examples for better understanding of trigonometric equation concepts. Example 1 : Find general solution of (2sinx – cosx)(1 + cosx) = \(sin^2x\) Solution : (2sinx – cosx)(1 + cosx) – (1 – \(cos^2x\)) = 0 \(\therefore\) (1 + cosx)(2sinx – cosx – 1 + cosx) = 0
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Here you will learn some straight line examples for better understanding of straight line concepts. Example 1 : Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14. Solution : Let the equation of line be \(x\over a\) + \(y\over b\) = 1
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Here you will learn some statistics examples for better understanding of statistics concepts. Example 1 : If mean of the seies \(x_1\), \(x^2\), ….. , \(x_n\) is \(\bar{x}\), then the mean of the series \(x_i\) + 2i, i = 1, 2, ……, n will be- Solution : As given \(\bar{x}\) = \(x_1 + x_2 +
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Here you will learn some sets examples for better understanding of sets concepts. Example 1 : The set A = [x : x \(\in\) R, x^2 = 16 and 2x = 6] equal- Solution : \(x^2\) = 16 \(\implies\) x = \(\pm\)4 2x = 6 \(\implies\) x = 3 There is no value of x
Here you will learn some sequences and series examples for better understanding of sequences and series concepts. Example 1 : If \({\sum}_{r=1}^{n} T_r\) = \(n\over 8\) (n + 1)(n + 2)(n + 3), then find \({\sum}_{r=1}^{n} \)\(1\over T_r\) Solution : \(\because\) \(T_n\) = \(S_n – S_{n-1}\) = \({\sum}_{r=1}^{n} T_r\) – \({\sum}_{r=1}^{n
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Here you will learn some scalar and vector examples for better understanding of scalar and vector concepts. Example 1 : Find the vector of magnitude 5 which are perpendicular to the vectors \(\vec{a}\) = \(2\hat{i} + \hat{j} – 3\hat{k}\) and \(\vec{b}\) = \(\hat{i} – 2\hat{j} + \hat{k}\). Solution : Unit vectors perpendicular to \(\vec{a}\) &
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Here you will learn some relations examples for better understanding of relation concepts. Example 1 : If A = {2, 4} and B = {3, 4, 5} then (A \(\cap\) B) \(\times\) (A \(\cup\) B) Solution : (A \(\cap\) B) = {4} and (A \(\cup\) B) = {2, 3, 4, 5} \(\therefore\) (A \(\cap\) B)
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