Calc II midterm review guide

• Aug 8th 2009, 02:27 PM
mikemurphy
Calc II midterm review guide
So here is the story. I offered to help a friend with a few problems that he did not understand so he dropped off the practice test and I was gonna do the problems and then explain to him how i solved them, the only problem is that i am lost on three problems, I took calc II at a community college and apperently we skipped a couple important sections. Thanks in advance.

I believe this is a dot product problem, but like i said i think my teacher skipped this.

a=<-4,0,3> b=<1,-2,2>

A.)|a|

B.)3a + b

C.)a . b

D.) the angle between a and b

E.) a X b

F.) comp (sub b) a

Given the point P(2,-2,0) and the line l with parametric equations x=2t, y=1-t z=3+t find the following.

A.) Parametric and symmetric equations of the line through P and parallel to the line l.

B.) an equation of the plane containing P and perpendicular to l

C.) the point of intersection of the given line l with the plane 2x-3y+z-4=0

and if you could set up this integral and i will evaluate it that would be a huge help.

Polar curves r=4cos2theta and r=2
1.)the integral for the area inside r=4cos2theta and outside r=2

2.)and the integral for the area common to both.

Thanks in advance i have one more question but ive actually resorted to facebooking my old calc teacher from high school to help me out. I feel bad asking for help but I am so lost and never learned this or seem to have forgotten it. If at all possible id like to have these done by sunday so i can explain it to him sunday night so on monday he can take his exam with all the info needed.
• Aug 8th 2009, 03:31 PM
eXist
A) |a| = magnitude = length of the vector.
To find the magnitude use the formula: $l = \sqrt{x_1^2 + x_2^2 + ... + x_n^2}$ where n is the number of coordinates you have (in this case 3).

B) Fairly simple: $3a + b = 3<-4, 0 , 3> + <1, -2, 2> = <-12, 0, 9> + <1, -2, 2>$ Scalars distribute through vectors like they do through parenthesis, then you just add the corresponding coordinates.

C) This is called the dot product: $a \cdot b = (a_1 * b_1) + (a_2 * b_2) + ... + (a_n * b_n)$ n being the number of coordinates you have, in this case 3 again. The result of the dot product should always be a scalar.

D) The formula: $cos \theta = \frac{a\cdot b}{|a||b|}$ can be used where $\theta$ is the angle between the vectors.

E) This is known as the cross product. It is only defined (that I know off) in three dimensional space $R^3$. Check out Cross product - Wikipedia, the free encyclopedia and look under computing the cross prodcut. They explain it better than I can.