Suppose vector u = <1,-5,5> and vector v = <3,3,2>  Use the triple scalar product to decide the following. <2, -28, 23> is coplanar or not coplanar with vector u and vector v

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tiburtius | High School Teacher | (Level 1) Educator

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If triple scalar product is equal to 0 then vectors are coplanar, otherwise they are not coplanar.

`<<1,-5,5>>(<<3,3,2>>xx<<2,-28,23>>)=det[[1,-5,5],[3,3,2],[2,-28,23]]=`

`|[3,2],[-28,23]|-3|[-5,5],[-28,23]|+2|[-5,5],[3,2]|=(69+56)-3(-115+140)+2(-10-15)=`

`125-75-50=0`

Since our triple product is equal to zero it follows that all three vectors are coplanar.

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