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Unformatted text preview: 1.5.2 Cartesian form of a plane in R3 You learnt from high school that an equation of a straight line can be written in the form ar+by+c = 0. Such an equation is called a linear equation in two variables. The set of all points (as, 3;) which satisfy the equation is a straight line. Now we define linear equations in n variables and interpret them geometrically in the special case n = 3. Definition 5.. A linear equation in as variables (or unknowns) $1,312, . . . ,3”, is an equation of the form (11331 + {12132 + - -- + ans?” 2 b, where all . . . ,an and b are scalars. 331 Only in R3, a plane can be described by a single linear equation. For x = 332 , consider the 373 linear equation in the three variables 2:1, 2:2, 3:3 given by {1331 + b.3132 +cas'3 = d, where a. b. c. d are fixed scalars. Now if o: i O. we can solve the eouation to find {171 in terms of ma ...
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