Question

Find the volume of the parallelepiped with a adjacent edges PQ, PR, and PS.

P(3, 0, 1), Q(-1, 2, 5), R(5, 1, -1), and S(2, -2, 2)

Answer 1

do u know how to Cross Product ?
a x b

Answer 2

yeah i know cross product

Answer 3

I need to use the scalar triple product?

Answer 4

Find the volume of the parallelepiped with a adjacent edges PQ, PR, and PS.
P(3, 0, 1), Q(-1, 2, 5), R(5, 1, -1), and S(2, -2, 2)
use 3x3 determinant
Find displacement vectors PQ,PR,PS with components by subtracting. That means PQ you subtract Ps from Qs:
P(3, 0, 1), Q(-1, 2, 5)
PQ = (-1-3,2-0,5-1) = <-4,2,4>
Can u solve for PR and PS

Answer 5

so which three do I use? PQR?

Answer 6

a picture would help out a lot as well. I am having a difficult time seeing it

Answer 7

You first find vectors PQ QR and RS

Answer 8

okay

Answer 9

i am working on it right now it will take me a few min

Answer 10

Work out the vectors PQ, PR and PS, then after that use the vector formula
\[V=|a*(b x c)|=|b*(c x a)|=|c*(a x b)|\]

Answer 11

PQ=<2,1,1> PR=<1,-1,2> PS=<0,-2,3>

Answer 12

do u understand how to do the vector formula i provided above?

Answer 13

not really

Answer 14

is abc the three vectors i found?

Answer 15

yes

Answer 16

a b c is the scalar triple product of three vectors a,b and c

Answer 17

okay i think i have it figured out

Answer 18

give me a sec to work it out

Answer 19

Keep that in mind, that scalar product is commutative

Answer 20

am i allowed to apply the cross product two any two vectors i found?

Answer 21

The vector triple product is defined as the cross product of one vector with the cross product of the other two.
http://en.wikipedia.org/wiki/Triple_product

Answer 22

http://www-math.mit.edu/~djk/18_022/chapter02/section02.html
this is a helpful website