Thread: Vectors - Parametric Equations

Earth is described by the equation : x + y + z = 18
Mars is described by the equation: 4x + 3y - z = -3

Earth and Mars intersect each other

a/ find a parametric equation of the line in which earth intersect mars

b/ The coordinate of Spring Lake is given by the point (-5, 10, 13)
How far away from spring lake from the line mentioned in (a)?

Hello, shiiganB!

Astronomically, the problem makes no sense,
. . but I'll solve it anyway.

Earth and Mars intersect each other.

(a) Find a parametric equation of the line in which Earth intersect Mars.

Add [1] and [2]: .

Substitute into [1]: .

. . We have: .


On the right, replace with the parameter

. . Therefore: .

(b) The coordinates of Spring Lake is given by the point (-5, 10, 13).
How far away from Spring Lake is the line mentioned in (a)?

A strange (silly!) question . . .

Spring Lake could be a ski resort located on Mars or Jupiter or . . .

Ignoring that possibility, Spring Lake is probably located on Earth,
. . in which case, it is on the line mentioned in (a).

. . The distance is zero.


To check, try