Question

10 Find the distance of point P (-7,0,5) from the straight line passing through points
A(-2,0,1) and B(3,2,2) .

Answer 1

slope between A and B maybe, then perp it ... might be easier said then done in that way tho

Answer 2

-2 0 1
-3-2-2
-------
-5 -2 -1 .... <5,2,1> is the vector between our points

Answer 3

line:
x=-2+5t
y= 0+2t
z= 1+ t

plane with out given point is:

5(x--7)+2(y-0)+1(z-5)=0

this line and this plane intersect at:

5(-2+5t+7)+2(0+2t-0)+1(1+ t-5)=0

25+25t+4t-4+ t=0

(25-4)+t(25+4+1)=0

(21)+t(30)=0 ; t=7/10 maybe

x=-2+5.7/10= 15/10
y= 0+2.7/10= 14/10
z= 1+ 7/10 = 17/10

so the distance between this point and the other might be it if I did the mathing roght

Answer 4

I,m still puzzled, whats the distance. the value for t

Answer 5

the distance in my case would be the distance formula using the point given and the found point; t was just used to find the needed point

Answer 6

a simpler method might be to employ a sin of the angle between vectors tho

Answer 7

AB and AP are 2 vectors; find the angle between them and the distance is AP sin(a)

Answer 8

Thats how they do it but i dont really know how do u.

Answer 9

I do it in whatever manner makes sense to me .... seeing how I do not have any material to base a solution on I have to pretty much make one up that will fit the bill

Answer 10

i try to understand how u did it. but whats the distance that u got

Answer 11

if my math is right, we can take our discovered point and subtract it from our known point

-7 , 0 , 5
-15/10, -14/10, -17/10

-70/10, 0/10, 50/10
-15/10, -14/10, -17/10
-----------------------
-85/10, -14/10, 33/10

square add amd sqrt the results

sqrt(85^2+14^2+33^2) /10 would be our distance, about 9.22

we can check this with the sine method to be sure :)

Answer 12

P (-7,0,5) B(3,2,2) .
-A(-2,0,1) -A(-2,0,1)
--------------------
a<-5,0,4> b<5,2,1>

|a| = sqrt(41) |b|=sqrt(30)

a<-5,0,4>
.b<5,2,1>
-----------
-25+0+4 = -21

cos(t) = -21/sqrt(41*30)

t = arccos(-21/sqrt(41*30))

|a| sin(t) = our distance than

d = sqrt(41) sin(arccos(-21/sqrt(41*30))) = 5.13

so that means my math is off someplace, or ive forgoteen a step :/