Hello.
so my task was to find the distance between point A(3,0,4) to plane (x+1)/3 = y/4 = (z-10)/6
So heres how i tried to do this
1) Found that direction vector is u = ( 3, 4, 6) and the normal vector is the same n = (3,4,6)
took the equation n * v = n * P
Or normal vector * any point on a plane is the same as n * the point.
So, (3,4,6) * (x,y,z) = (3,4,6) * (3,0,4)
3x + 4y + 6z = 33 //The equation of the plane
Then i transformed the cannonical equation to parametric.
x = 3t -1
y = 4t
z = 6t + 10
Then i inserted these values into the equation of the plane
3(3t-1) +4(4t) + 6(6t+10) = 33
And this is where everything starts to go tottaly wrong, at least i think so.
9t-3+16t+36t+6- = 33
61t = 33-60+3
61t = -24
t = -24/61 // This seems tottaly wrong.
So then i tried to get the point on the line that is perpendicular and on the same plane with the given point, but it just all seems to be going tottaly wrong....
P` = (3(-24/60)-1, 4(-24/61), 6(-24/61)+10)
So coordinates of the point P` are (-133/61, -96/61, 466/61)
Didn't realy go any further as this all seems so wrong to me... Am i doing everything ok or is there something im doing wrong?
Thank you.
so my task was to find the distance between point A(3,0,4) to plane (x+1)/3 = y/4 = (z-10)/6
So heres how i tried to do this
1) Found that direction vector is u = ( 3, 4, 6) and the normal vector is the same n = (3,4,6)
took the equation n * v = n * P
Or normal vector * any point on a plane is the same as n * the point.
So, (3,4,6) * (x,y,z) = (3,4,6) * (3,0,4)
3x + 4y + 6z = 33 //The equation of the plane
Then i transformed the cannonical equation to parametric.
x = 3t -1
y = 4t
z = 6t + 10
Then i inserted these values into the equation of the plane
3(3t-1) +4(4t) + 6(6t+10) = 33
And this is where everything starts to go tottaly wrong, at least i think so.
9t-3+16t+36t+6- = 33
61t = 33-60+3
61t = -24
t = -24/61 // This seems tottaly wrong.
So then i tried to get the point on the line that is perpendicular and on the same plane with the given point, but it just all seems to be going tottaly wrong....
P` = (3(-24/60)-1, 4(-24/61), 6(-24/61)+10)
So coordinates of the point P` are (-133/61, -96/61, 466/61)
Didn't realy go any further as this all seems so wrong to me... Am i doing everything ok or is there something im doing wrong?
Thank you.