Find parametric equations for a straight line parallel to the plane 3x-4y+7z=14?

Answer 1

Find parametric equations for a straight line parallel to the plane 3x - 4y + 7z = 14.
________

There are an infinite number of solutions to this problem. Any vector, whose dot product with the normal vector of the plane is zero, will suffice for the directional vector of a line that is parallel to the plane.

The normal vector n, of the plane is:

n = <3, -4, 7>

Let v be a vector whose dot product with n is zero. One solution is:

v = <1, -1, -1>

Now all we need is a point not in the plane.
Let's choose O(0,0,0).

One equation of a line parallel to the plane is:

L(t) = O + tv = tv
L(t) = t<1, -1, -1>
where t is a scalar ranging over the real numbers.

The parametric form of the equation of the line is:

L(t):
x = t
y = -t
z = -t

Answer 2

-4y+7z=20

Answer 3

3x-4y=20
3x+7z=20
-4y+7z=20

Answer 4

It is easy.Parallel to that plane means it is perpendicular to the normal of that plane.actually there are infinie lines which are parallel to a plane.Find 2 pts on the plane and find the direction ratios using them and its over

(0,0,2) and (1,-1,1) lie on this plane

the parametric eqns are

x=-t
y=t
z=t

If you want to verify this then see that this line and normal to the plane are perpendicular

(3i-4j+7k).(-i+j+k)=0

Answer 5

get three points, by making each variable 0 and solve