Question

how determine the value of x and y
such that points (1,2,3),(7,3,1),(x,y,2) are collinear

Answer 1

the ratio of parts are proportional

Answer 2

hi

Answer 3

hi

Answer 4

wat do u meam parts are proportional

Answer 5

mean

Answer 6

bad idea, i was thinking of parralel vectors:

create a line from the known parts

r = (1,2,3) + t(7,3,1)

x = 1 + 7t
y = 2 + 3t
z = 3 + t

determine (x,y,z) = (x,y,2)

Answer 7

ok

Answer 8

2 = 3+t ; t = -1

solve for x and y with t=-1

Answer 9

x=-6
t=-1
y=-1

Answer 10

thanks

Answer 11

youre welcome

Answer 12

hi
my answers are wrong

Answer 13

why?

Answer 14

se ΔPQR to answer the question.

What is tan P?

Answer 15

what you want for the equation of the line is a vector that points in the direction of the line

one way to find that vector is subtract 2 points on the line:

V= (7,3,1)- (1,2,3)= (6,1,-2)

the equation of the line is some point on the line, plus some amount of distance in the direction of V

for example:
P= (1,2,3) + t ( 6,1,-2)
if we set t= 0 we get point (1,2,3)
if we set t=1, we get point (7,3,1)

to find the x,y values to so that point (x,y,2) is on the line:
(x,y,2)= (1,2,3) * t (6,1,-2)

we need to find the correct value for "t"
one way: set the 3rd components equal: 2 = 3+ t*-2
we find t= 0.5
now you can find x and y:
x= 1+ 0.5*6= 4
y= 2+0.5*1= 2.5

test:
(1,2,3)+ 0.5*(6,1,-2)= (1,2,3)+ (3, 0.5, -1)= ( 4, 2.5, 2)

Answer 16

ok

Answer 17

thanks