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Find the Cartesian equation of a line passing through (1, -1, 2) and parallel to the line whose equations are x-3/1= y-1/2=z+1/-2 . Also, reduce the equation obtained in vector form.____

User Anku Singh
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Final answer:

To determine the Cartesian equation of a line parallel to X, we use the given direction ratios and the point through which the new line passes, resulting in the equation (x - 1)/1 = (y + 1)/2 = (z - 2)/-2 in symmetric form and vector form r = (1, -1, 2) + t(1, 2, -2).

Step-by-step explanation:

To find the Cartesian equation of a line passing through (1, -1, 2) and parallel to the given line, we must perform the following steps:

  1. Identify the direction ratios of the given line, which are the coefficients of the denominators in the given equations: (1, 2, -2).
  2. Since the required line is parallel to the given line, it will have the same direction ratios. Therefore, the required line will also have the direction vectors (1, 2, -2).
  3. Now, use the point (1, -1, 2) and the direction ratios to write the equation of the required line in the symmetric form:
    (x - 1)/1 = (y + 1)/2 = (z - 2)/-2
  4. Finally, rearrange this into the vector form of a line equation:
    r = (1, -1, 2) + t(1, 2, -2), where t is a parameter.

The vector form reduces to:

  • x = 1 + t
  • y = -1 + 2t
  • z = 2 - 2t

User Sebaferreras
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