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?
1 Answer | Add Yours
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.`
We’ve answered 319,812 questions. We can answer yours, too.Ask a question