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Show that the points P(a+2b+c),Q(a-b-c),...

Show that the points `P(a+2b+c),Q(a-b-c),R(3a+b+2c) and S(5a+3b+5c)` are coplanar given that a,b and c are non-coplanar.

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To show that the points \( P(a + 2b + c), Q(a - b - c), R(3a + b + 2c), S(5a + 3b + 5c) \) are coplanar, we can use the concept of vectors and determinants. The points are coplanar if the volume of the parallelepiped formed by the vectors connecting these points is zero, which can be determined using the scalar triple product. ### Step-by-Step Solution: 1. **Define the Points**: Let: \[ P = a + 2b + c, \quad Q = a - b - c, \quad R = 3a + b + 2c, \quad S = 5a + 3b + 5c ...
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