Find an equation of the plane passing through the point (0,0,6) perpendicular to x=1-t y=2+t z=4-2t

The equation of plane is x-y+z=12.

Step-by-step explanation:

It is given that the plane passing through the point (0,0,6) perpendicular to x=1-t y=2+t z=4-2t.

The given line is perpendicular to required plane, so coefficients of t represents the normal vector.

Normal vector is

If a plane passes through and having normal vector , then the equation of plane is

Multiply both sides by -1.

Therefore, the equation of plane is x-y+z=12.

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0