PreCalc
posted by John .
QP is (x y) = (3 1) + r (14 10)
QR is (x y) = (3 1) + s (17 9)
PR is (x y) = (0 18) + t (5 7)
where r, s, and t are scalars.
1. Use vector methods to find the coordinates of P, Q, and R.
2. Find vectors PQ and PR and evaluate PQ*PR
3. Find size of QPR
4. Find the area of triangle PQR

Your notation is slightly different from the one I am used to.
QP is a line with (x,y) = (3,1) + r(14,10)
or
x = 3 + 14r
y = 1 + 10r
PR:
x = 0 + 5t
y = 18  7t
P is the intersection of QP and PR
so
3 + 14r = 0 + 5t > 14r  5t = 3 **
1 + 10r = 18  7t > 10r + 7t = 19 ***
** times 7 > 98r  35t = 21
*** times 5 > 50r + 35t = 95
add them:
148r = 74
r = 1/2
then in
x = 3 + 14r > x = 3 + 7 = 10
y = 1 + 10r > y = 1 + 5 = 4
P is (10,4)
Find Q and R the same way.
(I bet Q is (3,1) , how do you think I found that without any work ??)
#2, I will do vector PQ
vector PQ = [310, 14] or [7,5]
if PQ*PR is the 'dot' product, then you should have a method in your text or notes, it is one of the easiest calculations
(in my notation, we use [....] for vectors and (...) for points )
#3 I don't know what you mean by "size" of QPR, to me that would mean area.
In that case what is the difference between #3 and #4 ?
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