Ex 11.2, 5 - Find equation of line in vector, cartesian form - Ex 11.2

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Ex 11.2, 5 Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2 + 4 and is in the direction + 2 . Equation of a line passing though a point with position vector and parallel to vector is = + Here, = 2 + 4 & = + 2 So, = (2 + 4 ) + ( + 2 ) Equation of line in vector form is (2 + 4 ) + ( + 2 ) Equation of a line passing though (x1, y1, z1) and parallel to a line having direction ratios a, b, c is 1 = 1 = 1 Since the line passes through a point with position vector 2 + 4 , 1 = 2, y1 = 1 z1 = 4 Also, line is in the direction of + 2 , Direction ratios : = 1, b = 2 , c = 1 Equation of line in Cartesian form is 2 1 = ( 1) 2 = 4 1 = + =

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