A directed segment  QR¯¯¯¯¯QR¯ with endpoints at  Q (2, 1)Q (2, 1) and  R (8, 13)R (8, 13) is partitioned from  QQ to  RR into a  1:21:2 ratio at point  ZZ.  What are the coordinates of  Z?

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Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

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Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

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Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…