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...

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?

 

Asked on by juno60

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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 `

`Z' =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.`

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