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mars1129 [50]
3 years ago
11

Not sure how to solve

Mathematics
1 answer:
Karolina [17]3 years ago
4 0

Answer:

  (x, y, z) = (13/7, 19/7, 25/7)

Step-by-step explanation:

You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.

The parametric equation for a line through (1, 1, 1) with this direction vector is ...

  (x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)

The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...

  (t +1) +2(2t +1) +3(3t +1) = 18

  14t +6 = 18

  t = 12/14 = 6/7

The point in the plane closest to (1, 1, 1) is ...

  (x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)

  (x, y, z) = (13/7, 19/7, 25/7)

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Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

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<u>Step-by-step explanation:</u>

Since (a, b) is equidistant from (-a, 2) and (2, -b), then it is the midpoint of the those two points. Use Midpoint formula to find (a, b).

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<em>Notice that I changed the equation to "negative 4" because the equation you provided did not make a true statement.</em>

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