## 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

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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?