If the line 
lies in the plane lx + my – z = 9, then find the value of l2 + m2?
We know that the lines 
lies in plane ax + by + cz + d = 0, then
a
Here,
x1 = 3, y1 = –2, z1 = –4 and l = 2, m = –1, n = 3
a = l, b = m, c = –1, d = –9
i.e, 3l + (– 2)m + (– 4)(– 1) – 9 = 0 and 2l – m – 3 = 0
3l – 2m = 5 and 2l – m = 3
3l – 2m = 5 …… (1)
2l – m = 3 ……(2)
Multiply eq.(1) by 2 and eq.(2) by 3 and then subtract we get
m = –1
l = 1
l2 + m2 = 2
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