Finding the Equation of a Perpendicular Line Through a Given Point

[andrey21]

Find the equation of the straight line which is perpendicular to the plane

4x+3y+2z=1

Which goes through the point (1,1,7)

Is the point (5,7,15) on this line?

By inspection we can see direction of the normal to the plane:

(4,3,2)

Therefore equation of straight line is:

r(t) = (1,1,7) + t (4,3,2)

Now I need to establish a value for t, however when I substitute in values for x,y,z I obtain:

t=1
t=2
t=4

Any help would be great thank you

 

[Mark44]

Find the equation of the straight line which is perpendicular to the plane

4x+3y+2z=1

Which goes through the point (1,1,7)

Is the point (5,7,15) on this line?

By inspection we can see direction of the normal to the plane:

(4,3,2)

Therefore equation of straight line is:

r(t) = (1,1,7) + t (4,3,2)

Now I need to establish a value for t, however when I substitute in values for x,y,z I obtain:

t=1
t=2
t=4

Any help would be great thank you

Solving the equation <5, 7, 15> = <1, 1, 7> + t<4, 3, 2> yields
5 = 1 + 4t
7 = 1 + 3t
15 = 7 + 2t

In the first equation, t = 1 is the solution. Since the value is not a solution of the other two equations, you should conclude that (5, 7, 15) is not a point on the line.

 

[andrey21]

Thank you mark 44

 

[Mark44]

You're welcome!