(#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