If the volume of the parallelopiped is 158 cu . units whose coterminus edges are given by the vectors a =( i + j +n k ), b =2 i +4 j -n k and c = i +n j +3 k , where n 0 , then the value of n is

Step-by-step solution

aligned & Volume of parallelopiped = | array ccc 1 & 1 & n 2 & 4 & -n 1 & n & 3 array |=158 & 1 (12+n^2 )-1(6+n)+n(2 n-4)-158 & 3 n^2-5 n-152=0 & (3 n+19)(n-8)=0 & n=8 aligned