The line `(x+6)/5=(y+10)/3=(z+14)/8`is the hypotenuse of an isoscelesright-angled triangle whose opposite vertex is `(7,2,4)dot`Then which of the following in not the sideof the triangle?a. `(x-7)/2=(y-2)/(-3)=(z-4)/6`b. `(x-7)/3=(y-2)/6=(z-4)/2`c. `(x-7)/3=(y-2)/5=(z-4)/(-1)`d. noneof theseA. `(x-7)/(2)=(y-2)/(-3)=(z-4)/(6)`B. `(x-7)/(3)=(y-2)/(6)=(z-4)/(2)`C. `(x-7)/(3)=(y-2)/(5)=(z-4)/(-1)`D. none of these

The line `(x+6)/5=(y+10)/3=(z+14)/8`is the hypotenuse of an isoscelesr

1.	The line `(x+6)/5=(y+10)/3=(z+14)/8`is the hypotenuse of an isoscelesright-angled triangle whose opposite vertex is `(7,2,4)dot`Then which of the following in not the sideof the triangle?a. `(x-7)/2=(y-2)/(-3)=(z-4)/6`b. `(x-7)/3=(y-2)/6=(z-4)/2`c. `(x-7)/3=(y-2)/5=(z-4)/(-1)`d. noneof theseA. `(x-7)/(2)=(y-2)/(-3)=(z-4)/(6)`B. `(x-7)/(3)=(y-2)/(6)=(z-4)/(2)`C. `(x-7)/(3)=(y-2)/(5)=(z-4)/(-1)`D. none of these
Answer» Correct Answer - c Given one vertex A(7,2,4) and line `(x+6)/(5)=(y+10)/(3)=(z+14)/(8)` General point on above line `B-=(5lamda-6,3lamda-10,8lamda-14)` Direction ratios of line AB are `lt5lamda-13,3lamda-12,8lamda-18gt` Direction ratios of line BC are `lt5,3,8gt` Since angle between AB and BC is `pi//4`, we have `cos""(pi)/(4)=((5lamda-3)+3(3lamda-12)+8(8lamda-18))/(sqrt(5^(2)+3^(2)+8^(2)).sqrt((5lamda-13)^(2)+(3lamda-12)^(2)+(8lamda-18)^(2)))` Squaring and solving we have `lamda=3,2` Hence, equation of lines are `(x-7)/(2)=(y-2)/(-3)=(z-4)/(6)` and `(x-7)/(3)=(y-2)/(6)=(z-4)/(2)`