Determine if the three vectors lie in similar plane or not, Mathematics

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Determine if the three vectors a^→ = (1, 4, -7), b^→ = (2, -1, 4) and c^→ = (0, -9, 18) lie in similar plane or not.

Solution

Thus, as we noted prior to this example all we need to do is calculate the volume of the parallelepiped formed through these three vectors. If the volume is zero they lie in similar plane and if the volume is not zero they do not lie in similar plane.

226_Determine if the three vectors lie in similar plane or not.png

Thus, the volume is zero and so they lie in similar plane.

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