Show that the lines and are coplanar. Also, find the equation of the plane containing them.

we know that line and are coplanar if


And equation of the plane containing them is



Here, equation of lines are


and


So, x1 = – 1, y1 = 3, z1 = – 2, l1 = – 3, m1 = 2, n1 = 1


x2 = 0, y2 = 7, z2 = – 7, l2 = 1, m2 = – 3, n2 = 2


so,





= 1(4 + 3) – 4(– 6 – 1) – 5(9 – 2)


= 7 + 28 – 35


= 0


So, lines are coplanar


Equation of plane containing line is



(x + 1)(4 + 3) – (y – 3)(– 6 – 1) + (z + 2)(9 – 2) = 0


7x + 7 + 7y – 21 + 7z + 14 = 0


7x + 7y + 7z = 0


X + y + z = 0


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