If i know that the coordinate of one of vertex is Z(0,0,0), what are the other verticies?
Three vectors f= <1,6,4> g= <4,8,6> and k= <-2,4,5> form a parallelpiped. If i know that the coordinate of one of vertex is Z(0,0,0) What are the other verticies?
You need to picture the parallelipiped and you should consider Z(0,0,0) the lower left corner vertex.
You need to consider the vector `bar f` as the length of base rectangle, `barg` the width of rectangle and`bark` , the height of parallelipiped.
You need to use the following notation for the vertices of parallelipiped such that: A is the lower right vertex, B is the upper right vertex and C is the upper left vertex (right above the vertex Z).
The upper rectangle has the correspondent vertices Z',A',B'C'.
You may find the vertex A such that:
`A = bar f + Z = lt1,6,4gt + lt0,0,0gt = lt1,6,4gt`
You may find the vertex B such that:
`B = A + bar g = lt1,6,4gt + lt4,8,6gt `
`B = lt5,14,10gt`
You may find the vertex C such that:
`C = Z + barg = lt0,0,0gt + lt4,8,6gt `
`C = lt4,8,6gt`
You may find the vertex Z' such that:
`Z' = Z + bark = lt0,0,0gt + lt-2,4,5gt `
You may find the vertex A' such that:
`A' = A + bark `
`A' = lt1,6,4gt + lt-2,4,5gt`
`A' = lt-1,10,9gt`
You may find the vertex B' such that:
`B' = B + bark `
`B' = lt5,14,10gt + lt-2,4,5gt`
`B' = lt3,18,15gt`
You may find the vertex C' such that:
`C' =C + bark`
`C' = lt4,8,6gt + lt-2,4,5gt`
`C' = lt2,12,11gt`
Hence, evaluating the vertices of parallelipiped under given conditions yields `Alt1,6,4gt ;B lt5,14,10gt; C lt4,8,6gt ; Z' lt-2,4,5gt ; A' lt-1,10,9gt ; B' lt3,18,15gt ; C' lt2,12,11gt.`