If u = -2 + k , v =3 + k and w = - k , then the volume of the parallelopiped with u v , u + w and v + w as coterminus edges is

Step-by-step solution

u v = | array ccc i & j & k 1 & -2 & 1 3 & 0 & 1 array |= i (-2)- j (1-3)+ k (0+6)=-2 i +2 j +6 k u + w = i - j v + w =3 i + j aligned Volume of parallelopiped &=( u v ) [( u + w ) ( v + w )] &= | array ccc -2 & 2 & 6 1 & -1 & 0 3 & 0 & 1 array |=|-2(-1)-2(1)+6(-3)|=18 aligned