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(#18837372) Consider the points

`A(-6,2,1),B(3,10,2)`

, and

`C(-1,0,3)`

. Use the Show My Work file upload to attach a scan/image of your written work. a) Determine the vectors

`vec(u)=vec(AB)`

and

`vec(v)=vec(AC)`

. (5 pts)

`vec(u)=(:,◻,◻:)`

. \rangle b) Determine the vector

`vec(n)`

that is perpendicular to both

`vec(u)`

and

`vec(v)`

. (5 pts)

`q,`

c) Determine the equation of the plane that passes through the given points, expressed in

`ax+by+cz=d`

form. (5 pts)

`x+◻,z=◻`

d) Check your answers by computing

`vec(u),vec(v)`

and

`vec(n)`

using GeoGebra. Then graph your plane equation along with the vectors and given points. Create a new GeoGebra document and paste the Share link in the Show My Work textbox. ( 5 pts) GeoGebra Instructions Open a new GeoGebra 3D graph. Enter the first point by typing the expression "

`A=(-6,2,1)`

." Repeat for points

`B`

and

`C`

. Compute vector

`vec(u)`

by entering the expression "

`u=vector(A,B)`

." Repeat for

`vec(v)`

. Use the cross product command to compute

`vec(n)`

. Type in your plane equation to add it to the graph. The vector computation results in GeoGebra should match your written results. On the graph, you should see that all 3 points line on the plane, that

`vec(u)`

and

`vec(v)`

correctly connect the pairs of points, and that

`vec(n)`

is