I have a Point P(0,-1,1)

and a level

x+2=0

y-2z+4=0

i need to find the distance of the line between the level and the point P.

also the equationof this line.

Sorry, if the question is hard to understand, never done maths in english.

Guest Dec 7, 2017

#2**+1 **

I don't know what you mean by 'the level'.

Each of the two equations is the equation of a plane.

x+2 = 0, (x = -2) is a plane parallel with the yz plane passing through the point x = -2.

For the other, begin by thinking of the straight line z = (y + 4)/ 2 in the yz plane and then extending this, by shifting the yz plane parallel to itself for all values of x, (if that makes sense ?).

The straight line is the intersection of these two planes, so in effect the two equations taken together are the equation of the line.

The equation of the line can also be expressed parametrically, x = -2, y = 2t - 4, z = t, where t is the parameter,

You can think of this as being a single point, so the final part of the question is to calculate the value of t that minimises the distance of this point to your point P(0, -1, 1).

Tiggsy

Guest Dec 7, 2017

#1**0 **

To maybe elaborate what the 2 equations are, they are supposed to be levels.

n1xn2=(0;2;1)

Guest Dec 7, 2017

edited by
Guest
Dec 7, 2017

#2**+1 **

Best Answer

I don't know what you mean by 'the level'.

Each of the two equations is the equation of a plane.

x+2 = 0, (x = -2) is a plane parallel with the yz plane passing through the point x = -2.

For the other, begin by thinking of the straight line z = (y + 4)/ 2 in the yz plane and then extending this, by shifting the yz plane parallel to itself for all values of x, (if that makes sense ?).

The straight line is the intersection of these two planes, so in effect the two equations taken together are the equation of the line.

The equation of the line can also be expressed parametrically, x = -2, y = 2t - 4, z = t, where t is the parameter,

You can think of this as being a single point, so the final part of the question is to calculate the value of t that minimises the distance of this point to your point P(0, -1, 1).

Tiggsy

Guest Dec 7, 2017