Distance Between Two Parallel Lines If two lines are parallel, then they have the same distance between them throughout, Therefore the distance between two parallel lines \(ax + by + c_1\) and \(ax + by + c_2\) is given by : D = \(|c_1 – c_2|\over \sqrt{a^2 + b^2}\) Note – Both equation must be […]
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There are two conditions of concurrency of lines which are given below : (a) Three lines are said to be concurrent if they pass through a common point i.e. they meet at a point. Thus, Three lines \(a_1x + b_1y + c_1\) = 0 and \(a_2x + b_2y + c_2\) = 0 and \(a_3x + b_3y
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Let \(\vec{a}\) and \(\vec{b}\) be two non-zero vectors inclined at an angle \(\theta\). Then the scalar product or dot product of two vectors, \(\vec{a}\) with \(\vec{b}\) is denoted by \(\vec{a}\).\(\vec{b}\) and is defined as, \(\vec{a}\).\(\vec{b}\) = \(|\vec{a}||\vec{b}|cos\theta\) If \(\vec{a}\) = \(a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\) and \(\vec{b}\) = \(b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\). Then \(\vec{a}\).\(\vec{b}\) = \(a_1b_1+a_2b_2+c_1c_2\) Properties of Dot Product of Two
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Cross Product of Vectors Formula : Let \(\vec{a}\) & \(\vec{b}\) are two vectors & \(\theta\) is the angle between them, then cross product of vectors formula is, \(\vec{a}\) \(\times\) \(\vec{b}\) = |\(\vec{a}\)||\(\vec{b}\)|sin\(\theta\)\(\hat{n}\) where \(\hat{n}\) is the unit vector perpendicular to both \(\vec{a}\) & \(\vec{b}\). Properties of Vector Cross Product : (i) \(\vec{a}\) \(\times\) \(\vec{b}\) =
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Here, you will learn what is trigonometric equation and how to find general solution of trigonometric equation with examples. Let’s begin – An equation involving one or more trigonometrical ratios of unknown angles is called a trigonometrical equation. Solution of Trigonometric Equation A value of the unknown angle which satisfies the given equation is called
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Here you will learn what is conjugate hyperbola, equation of conjugate hyperbola and basic definitions of like eccentricity and latus rectum. Let’s begin – What is Conjugate Hyperbola ? The hyperbola whose transverse & conjugate axes are respectively the conjugate and transverse axes of given hyperbola is called the conjugate hyperbola of given hyperbola. The
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Here you will learn what is hyperbola, equation of the hyperbola and graph of a hyperbola with basic definitions like vertex, foci and directrix. Let’s begin – What is Hyperbola ? A hyperbola is the locus of a point in a plane which moves in a plane in such way that the ratio of its
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What is a Circle ? A circle is the locus of a point which moves in a plane in such way that its distance from a fixed point(in the same given plane) remains constant. The fixed point is called center of circle and the constant distance is called radius of the circle. The general equation
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A parabola is locus of a point which moves in a plane, such that its distance from a fixed point called focus is equal to its perpendicular distance from a fixed straight line called directrix. Graph of a Parabola and their types are shown below. Basic Concepts of a Parabola (a) Focal distance : The
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Here you will learn what is unit vector, representation of unit vector, formula for unit vector and how to find the unit vector with examples. Let’s begin – What is a Vector ? A quantity that has both magnitude & direction is called a vector. A vector that has magnitude of 1 is called a
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