Question

Distance of the plane 7x + 8y + 2z = 12 from origin is

(A) \(\frac7{\sqrt{117}}\)

(B) \(\frac8{\sqrt{117}}\)

(C) \(\frac2{\sqrt{117}}\)

(D) \(\frac{12}{\sqrt{117}}\) 

Answer 1

Correct option is (D) \(\frac{12}{\sqrt{117}}\)  

Distance of origin from plane 7x + 8y + 2z - 12 = 0 is 

\(d = \left|\frac{7\times 0 + 8\times 0 + 2\times 0 -12}{\sqrt {7^2 + 8^2 +2^2}}\right|\)

\(= \frac{12}{\sqrt {49 + 64 + 4}}\)

\(= \frac{12}{\sqrt {117}}\)