The altitude of parallelopiped whose three coterminous edges are the vectors, A→=i^+j^+k^;B→=2i^+4j^−k^ and C→=i^+j^+3k^ with A→ and B→ as the sides of  the base of the parallelopipied, is

h  =  A→ B→ C→|A→  ×B→|  and  | A→  ×B→|   =   a→2 b→2 − (a→ ⋅ b→)2a→2 b→2 − (a→ ⋅ b→)2=3 ×21-(2+4-1)2=63-25=38A→ × B→= -5i^+3j^+2k^A→ B→ C→=A→ × B→.C→=-5i^+3j^+2k^· i^+j^+3k^=4∴h=438=43838=23819