1. Equation of a plane passing through the points (6, -1, 1),(5, 1, 2) and (1, -5, 4)
⇒ (x – 6)(-10 + 4) – (y + 1)(5 + 5) + (z – 1)(4 + 10) = 0
⇒ (x – 6)(-6) – (y + 1)(10) + (z – 1)(14) = 0
⇒ -6x + 36 – 10y – 10 + 14z – 14 = 0
⇒ 6x +10y – 14z -12 = 0.
2. Dr’s normal to the plane are 6 : 10 : -14 ⇒ 3 : 5 : -7.
3. Since the dr’s normal to the plane are 3 : 5 : -7, a unit vector in this direction is
\(\frac{3i+5j-7k}{\sqrt{3^2+5^2+(-7)^2}} = \frac{3i+5j-7k}{\sqrt{83}}\)
