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Section 12.4: Cross Product

Exercise 45

  1. Let P be a point not on the line L that passes through the points Q and R. Show that the distance \(d\) from the point P to the line L is \[ d = \frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}|} \] where \(\mathbf{a} = \vec{QR}\) and \(\mathbf{b} = \vec{QP}\).
  2. Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 6, 8) and R(-1, 4, 7).