Question 1201853
a. Determine the Cartesian equation of the plane that contains the three points A(-2,3,1), B(3,4,5) and C(1,1,0).
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<pre>
     |-2   3   5|
D =  | 3   4   5|
     | 1   1   0|
</pre>
D = 24
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<pre>
     | 1   3   5|
a =  | 1   4   5| = 7
     | 1   1   0|
</pre>
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<pre>
     |-2   1   5|
b =  | 3   1   5| = 17
     | 1   1   0|
</pre>
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<pre>
     |-2   3   1|
c =  | 3   4   1| = -13
     | 1   1   1|
</pre>
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---> 7x + 17y -13z = 24
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This is easily done with an Excel sheet.
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b. Determine the Cartesian equation of the plane containing the point P(-1,1,0) and perpendicular to the line between the points A(1,2,1) and B(3,-2,0).