Question

The plane 2x + y + 2z = 9 intersects the coordinate axes at A, B, C. The orthocentre of the triangle ABC is –

• A. $\left( \frac { 9 } { 7 } , \frac { 27 } { 7 } , \frac { 9 } { 7 } \right)$
• B. $\left( \frac { 3 } { 13 } , \frac { 1 } { 13 } , \frac { 3 } { 13 } \right)$
• C. $\left( \frac { 3 } { 2 } , 3 , \frac { 3 } { 2 } \right)$
• D. (2, 1, 2)

Answer 1

Answer: (D)

(2, 1, 2)

Answer 2

A = $\left( \frac { 9 } { 2 } , 0,0 \right)$ , B = (0, 9, 0), C = $\left( 0,0 , \frac { 9 } { 2 } \right)$

If (a, b, g) is the orthocentre, AO ^ BC,

BO ^ CA, CO ^ AB, Ž a = g = 2b. (a, b, g) is a point on the given plane Ž a = g = 2, b = 1

\ O = (2, 1, 2)