# (Solved): (#18837372) Consider the points A(-6,2,1),B(3,10,2), and C(-1,0,3). Use the Show My Work file upload ...

(#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=◻

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

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