Q33 of 33 Page 11

Show that the lines and are coplanar. Hence, find the equation of the plane containing these lines.

We know that the lines are coplanar if


Here,


x1 = –3, x1 = –1, y1 = 1, y2 = 2, z1 = 5, z2 = 5


l1 = –3, l2 = –1, m1 = 1, m2 = 2, n1 = 5, n2 = 5




= 2(–5) – 1(–10) = – 10 + 10


= 0


So the given line are coplanar .


The equation of plane contains lines is


(x + 3)(5 – 10) – (y – 1)(– 15 – (– 5)) + (z – 5)(– 6 – (– 1)) = 0


– 5x – 15 + 10y – 10 – 5z + 25 = 0


– 5x + 10y – 5z = 0


Divided by – 5


x – 2y + z = 0

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