Practice Exam for First Midterm
This is a practice exam for the first midterm. Feel free to drop any comment or question below. I will try to answer here as many as possible, until the day of the exam. Good luck!
- [5 pts] Find the lengths of the sides of the triangle
where
and
- [10 pts] Find an equation of the sphere that passes through the origin and whose center is
- [5 pts] Find a vector that has the same direction as
but has length 6.
- [10 pts] For what values of
are the vectors
and
orthogonal?
- [10 pts] Compute the length of the curve
for
- [5 pts] Find the volume of the parallelepiped with adjacent edges
and
where
and
- [5 pts] Find a non-zero vector orthogonal to the plane through the points
and
- [10 pts] Where does the line through
and
intersect the plane
- [10 pts] Find the distance from the point
to the line
- [10 pts] Compute the limit
- [10 pts] Find parametric equations for the tangent line to the curve
at the point
- [10 pts] Find the curvature of
at the point
Francisco Blanco-Silva 
are we allowed to use calculators on the exam
Will we be allowed to use calculators on the exam? (Sorry if this is a duplicate, but I’m not sure if the first comment went through or not.)
Nope. No books, notes or calculators.
Is there a way to check if we found the correct answers to these questions?
Did anyone get an answer for number nine, i got the answer to be 7.
how do you find the directional vector for #11
how do you find the directional vector for #11?
you have to take the derivative of r(t) so you get r'(t)=(x’i+y’j+z’k)…. then you plug in the x_0 y_0 and z_0 values of the given point for t in the derivatives that correspond with it… By doing this we are finding the a b and c values we need for our parametric equations. Since we are already given the point we already have our x_0, y_0, and z_0…. now you have all you need to solve if I didnt skip anything…
x=x_0+at y=y_0+bt z=z_0+ct
Are we allowed to have a cheat sheet?
No
Just gunna throw out my answers for the ones that I have attempted in case any one wants to compare. #1. PQ=6, QR=sqrt(40), RP=6.
#2. (x-1)^2 + (y-2)^2 + (z-3)^2 = 14.
#3.
#4. b=0 and b=2
#5. ?
#6. ?
#7. 13i -14j +5k
#8. P(7,-4,3)
#9. 7
and thats as far as I’ve gone.
-John Jackson
What did everyone get for 7?
Find the directional vectors for sides PQ and QR. Compute PQ x QR. That should be the answer you’re looking for.
did anyone else get sqrt(76)/(14*sqrt(14)) for 12?
I got the same thing
I got but I may be wrong
13, -14 , 5 is what I got for 7. The numbers didn’t go through the first time
I know this is late notice but does anyone know if we have to know the all the different quadric surfaces?