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