(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=dform. (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
Band
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
