Question

Given the points A(1,0,-1), B(2,-3,5), and C(0,5,1) in R^3 answer the following:

i Find the angle, a (alfa), between the line segment AB and AC.

ii Find the area of the triangle in space determined by A,B and C.

iii Find parametric equation of the line L that contains the point A and is parallel to the line with symmetric equation x-3/4=y/2=z+2/-1

Answer 1

i need to find the magnitude of the two lines then use tan(theta)?

Answer 2

for part i

Answer 3

first use distance formula to get side lengths
AB = sqrt46
AC = sqrt30
BC = 2sqrt21

i would use law of cosines to find angle alpha

Answer 4

Do you have the formula for law of cosine

Answer 5

distance formula is x^2+y^2+z^2?

Answer 6

\[c^{2} = a^{2} +b^{2}-2ab \cos C\]
a,b,c are sides .... C is angle opp of side "c"

distance formula
\[d = \sqrt{(x_2 -x_1)^{2}+(y_2 -y_1)^{2}+(z_2 -z_1)^{2}}\]

Answer 7

okay thanks

Answer 8

you can use herons formula for the area

Answer 9

herons formula?

Answer 10

i am going to solve part i really quick

Answer 11

k, ill post the formula

Answer 12

thanks man

Answer 13

\[\text{given the length of the three sides a, b and c }\\then\\Area = \sqrt{s(s-a)(s-b)(s-c)}\\where \space s \space = \frac{a+b+c}{2}\]

Answer 14

The calc book they offer us at the college doesn't explain this material very well. I am trying to figure out which section in the book this question would be asked

Answer 15

this is zach

Answer 16

I know it's zach'

Answer 17

ahh no need to tell me about the book then:P

Answer 18

ah I c what your saying, this is calc 4 stuff

Answer 19

So this question is not from the book?