Question

Are the Points P(1,-1,-1) Q(3,1,-1) R(0,2,1) and S(-2,0,1) are coplanar, justify.

Answer 1

Answer:

no

Step-by-step explanation:

$let \: in \: vector \: form\\ \: \: a1 = i - j - k \\ a2 = 3i + j - k \\ b1 = 2i + k \\ b2 = - 2i + k \\ now \\ \: \: using \: coplanarity \: formula \\ (a2 - a1).b1 \times b2 = 0 \\ since \: \\ a2 - a1 = 2i + 2j \\ and \: b1 \times b2 = 2i - 2j + 4k \\ now \\ (2i + 2j).(2i - 2j + 4k)is \: not \: equal \: to \: 0 \\ so \: a2 - a1 \: is \: not \: perpendicular \: to \: b1 \times b2.$