# maths

posted by .

Find the point on line x+2/3=y+1/2=z-3/2 at a distance 5 units from the point P(1,3,3)....pllz help me out.

• maths -

Let the new point be (x1, y1, z1)

Then, using the distance formula:

((x1-1)^2 + (y1-3)^2 + (z1-3)^2)^0.5 = 5

(x1-1)^2 + (y1-3)^2 + (z1-3)^2 = 25

Put all units in terms of one variable. I'm choosing x1 first:

x1+2/3 = y1+1/2; y1 = x1 + 2/3 - 1/2
= x1 + 1/6

x1 + 2/3 = z1-3/2; z1 = x1 + 2/3 + 3/2 = x1 + 4/6 + 9/6 = x1 + 13/6

(x1-1)^2 + (x1+1/6-3)^2 + (x1+13/6-3)^2 = 25

Multiply this out; solve for x1; then plug these back into the other equations to solve for y1 and z1

## Similar Questions

1. ### Physics

The drawing shows four point charges. The value of q is 2.4 µC, and the distance d is 0.86 m. Find the total potential at the location P. Assume that the potential of a point charge is zero at infinity. This is a question of electric …
2. ### math

line xy is translated 3 units to the left. if a point on line xy is located at (2,11), where would the equivalent point be on line X and Y prime?
3. ### calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
4. ### math

A straight line AB of length 10 units is free to move with its ends on the axes. Find the locus of a point P on the line at a distance of 3 units from the end on the x axis.
5. ### Maths

Find the equation of the locus of the point P(x,y) which moves so that it's distance from the point (0,3) is equal to its distance from the line y=-3 Show that the point (-6,3) lies on the locus Please help me with thisand also show …
6. ### geometry

a point F is at a certain distance from a line AB .Another point P is moving in a plane such that the ratio of it's distance from F and line AB remains constant .find the locus of the point P
7. ### heeeeeelp maths

An ant is walking along the cartesian plane. It starts at the point A=(−18,8) walks in a straight line to a point on the x-axis, walks directly to the right for 7 units and then walks in a straight line to the point B=(9,13). …
8. ### Math

A line 'l' intersects line 'm' at point A at 45 degree angle. B and C are points on line m, where the distance from B to A is equal to the distance from A to C. How many points on line 'l' are equidistant from points B and C?
9. ### Precalculus

Find every point on the horizontal line y = 5 that is a distance of 5 units away from the point (6, 1).
10. ### Linear algebra

Let L1 be the line passing through the point P1=(−1, −1, 8) with direction vector →d1=[1, 0, −3], and let L2 be the line passing through the point P2=(7, −11, 14) with direction vector →d2=[1, 2, −3]. Find the shortest …

More Similar Questions