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Converting Vector Equations to Cartesian Equations and Vice Versa

Learn how to convert between vector and Cartesian equations easily with step-by-step examples and explanations. Master the process of finding equations in both forms effortlessly.

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Converting Vector Equations to Cartesian Equations and Vice Versa

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  1. ( ) ( ) ( ) x = 2 + t 1 y -3 + 2 Finding the Cartesian Equation from a vector equation x = 2 + t y = -3 + 2t t = x – 2 t = (y + 3)/2 x – 2 = y + 3 2 2x – 4 = y + 3 y – 2x + 7 = 0

  2. ( ) X = 4 + t 3 y 1 + 5 ( ) ( ) Finding the Cartesian Equation from a vector equation x = 4 + 3t y = 1 + 5t t = (x – 4) / 3 t = (y - 1) / 5 x – 4 = y - 1 3 5 5x – 20 = 3y - 3 3y – 5x + 17 = 0

  3. ( ) X = -2 + t 3 y -9 + 5 ( ) ( ) ( ) 3 5 ( ) 1 5/3 Finding the Vector Equation from a Cartesian equation 3y – 5x + 17 = 0 x = -2 y = -9 So (-2, -9 ) is on the line Gradient is 5/3 so vector in the line is or

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