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Use normal vectors to determine the interaction, if any, for each of the following pairs of...

Use normal vectors to determine the interaction, if any, for each of the following pairs of planes. Give a geometric interpretation in each case and the number of solutions for the corresponding system of linear equations. If the planes intersect in a line, determine a vector equation of the line.

  1. x + 2y + 3z = −4
    2x + 4y + 6z = 10
  2. 2x − y + 2z = −8
    4x − 2y + 4z = −16
  3. x + 3y − 5z = −12
    2x + 3y − 4z = −6
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