Question

Let the points on the plane P be equidistant from the points (–4, 2, 1) and (2, –2, 3). Then the acute angle between the plane P and the plane 2x + y + 3z = 1 is

• A. \(\frac{π}{6}\)
• B. \(\frac{π}{4}\)
• C. \(\frac{π}{3}\)
• D. \(\frac{5π}{12}\)

Answer 1

The Correct Option is C

Let \(P(x, y, z)\) be any point on plane \(P_1\)

Thereafter,  \((x+4)^2+(y−2)^2+(z−1)^2=(x−2)^2+(y+2)^2+(z−3)^2\)

\(⇒12x−8y+4z+4=0\)

\(⇒3x−2y+z+1=0\)

Also,  \(P_2 : 2x + y + 3z = 1\)

\(p_ 1\;and  \; p_2\) create the angle of 

\(Cos θ = | \frac{6-2+3}{14}|\)

\(⇒ θ = \frac{π }{ 3}\)

Hence, the correct option is (C): \(\frac{π}{3}\)