Let the plane x + 3 y - 2 z + 6 = 0 meet the co-ordinate axes at the points A , B , C . If the orthocenter of the triangle A B C is α , β , 6 7 , then 98 α + β 2 is equal to __________.

Step-by-step solution

Given, The plane x + 3 y - 2 z + 6 = 0 meet the co-ordinate axes at the points A ,   B ,   C , So, A - 6 , 0 , 0 ,   B 0 , - 2 , 0   &   C 0 , 0 , 3 And the orthocenter of the triangle A B C is α ,   β ,   6 7 , We know that, circumcentre of triangle is point of intersection of perpendicular bisectors, So, plotting the diagram we get, Now from diagram we can see that O  to midpoint of   B C   ⊥   B C So, by perpendicular vector for