If the planes 2 x+3 y+4 z+7=0 and 4 x+k y+8 z+1=0 are parallel, then the equation of the plane passing through is point ( k , k , k ) and having the direction ratios of its normal as ( k -1, k , k +1) is

Step-by-step solution

Since given planes, 2 x+3 y+4 z+7=0 and 4 x+k y+8 z+1=0 are parallel Hence 2 4 = 3 k k=6 Hence now the required plane through point (k, k, k) and having the direction ratios of its normal as (k-1, k, k+1) is aligned & a (x-x₁ )+b (y-y₁ )+c (z-z₁ )=0 & (k-1)(x-k)+k(y-k)+(k+1)(z-k)=0 & 5(x-6)+6(y-6)+7(z-6)=0 & 5 x+6 y+7 z=108 aligned