Finding the volume of a parallel pipedGiven the points P ( − 2 , 3 , 1 ) , Q ( 2 , − 2 , 0 ) , R ( 4 , 1 , 0 ).Find the parallelepiped with edge OP,OQ,OR where O is the origin (0,0,0).Volume for a parallelepiped is V = A × B ⋅ C.So would the volume be O P ⋅ ( O Q × O R ). &lt; − 2 , 3 , 1 &gt; ⋅ ( &lt; 2 , − 2 , 0 &gt; × &lt; 4 , 1 , 0 &gt; ) &lt; 2 , 3 , 1 &gt; ⋅ &lt; 0 , 0 , 10 &gt;area parallelepiped is 10 but would this be correct?

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Finding the volume of a parallel pipedGiven the points   P  (  −  2  ,  3  ,  1  )  ,  Q  (  2  ,  −  2  ,  0  )  ,  R  (  4  ,  1  ,  0  ).Find the parallelepiped with edge OP,OQ,OR where O is the origin (0,0,0).Volume for a parallelepiped is   V  =  A  ×  B  ⋅  C.So would the volume be   O  P  ⋅  (  O  Q  ×  O  R  ).  &amp;lt;  −  2  ,  3  ,  1  &amp;gt;  ⋅  (  &amp;lt;  2  ,  −  2  ,  0  &amp;gt;  ×  &amp;lt;  4  ,  1  ,  0  &amp;gt;  )  &amp;lt;  2  ,  3  ,  1  &amp;gt;  ⋅  &amp;lt;  0  ,  0  ,  10  &amp;gt;area parallelepiped is 10 but would this be correct?

yorbakid2477w6 · Accepted Answer

Step 1Looks like you&#039;ve done it correctly.The volume of a parallelepiped with three vectors from one vertex             P      →        ,            Q      →        ,            R      →       is the triple product   V  =            P      →        ⋅  (            Q      →        ×            R      →        ):Step 2  V  =  (  −  2            x      ^        +  3            y      ^        +            z      ^        )  ⋅  (  (  2            x      ^        −  2            y      ^        )  ×  (  4            x      ^        +            y      ^        )  )  V  =  (  −  2            x      ^        +  3            y      ^        +            z      ^        )  ⋅  10            z      ^        =  10.

cousinhaui · Accepted Answer

Step 1Alternately, the volume can be found as (the absolute value of) the determinant of the matrix,      [                            −          2                          3                          1                                      2                          −          2                          0                                      4                          1                          0                      ]    ,, which is fairly simple to find via cofactor expansion down the third column.Step 2(The determinant approach has the added benefit of being generalizable to n-dimensional parallelpipeds for   n  ≠  3.)

Given the points P(-2,3,1), Q(2,-2,0), R(4,1,0). Find the parallelepiped with edge OP, OQ, OR where O is the origin (0,0,0). Volume for a parallelepiped is V=A times B cdot C

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