If the plane `2x-y+2z+3=0` has the distances `(1)/(3)` and `(2)/(3)` units from the planes `4x-2y+4z+lambda=0` and `2x-y+2z+mu=0`, respectively, then the maximum value of `lambda+mu` is equal toA. 13B. 15C. 5D. 9

If the plane `2x-y+2z+3=0` has the distances `(1)/(3)` and `(2)/(3)` u

1.	If the plane `2x-y+2z+3=0` has the distances `(1)/(3)` and `(2)/(3)` units from the planes `4x-2y+4z+lambda=0` and `2x-y+2z+mu=0`, respectively, then the maximum value of `lambda+mu` is equal toA. 13B. 15C. 5D. 9
Answer» Correct Answer - A Equation of given planes are `2x-y+2z+3=0" "…(i)` `4x-2y+4z+lambda=0" "...(ii)` and `" "2x-y+2x+mu=0" "...(iii)` `because`Distance between two parallel planes `ax+by+cz+d_(1)=0` and`" "ax+by+cz+d_(2)=0` is distance`=(\|d_(1)-d_(2)\|)/(sqrt(a^(2)+b^(2)+c^(2)))` `:.`Distance between planes (i) and (ii) is `(\|lambda-2(3)\|)/(sqrt(16+4+16))=(1)/(3)" "["given"]` `implies\|lambda-6\|=2implies" "lambda-6=+-2implieslambda=8" or "4` and distance between planes (i) and (iii) is `(\|mu-3\|)/(sqrt(4+1+4))=(2)/(3)" "["given"]` `implies" "\|mu-3\|=2` `implies" "mu-3=+-2impliesmu=5` or 1 So, maximum value of `(lambda+mu)` at `lambda=8` and `mu=5` it is equal to 13.

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If the plane `2x-y+2z+3=0` has the distances `(1)/(3)` and `(2)/(3)` units from the planes `4x-2y+4z+lambda=0` and `2x-y+2z+mu=0`, respectively, then the maximum value of `lambda+mu` is equal toA. 13B. 15C. 5D. 9

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