Determine the cartesian equation of the plane that is perpendicular to the plane x-2y+z=6 and contains the line (x,y,z) = (2,-1,-1) + t(3,1,2).
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
We have to find the Cartesian equation of the plane that is perpendicular to the plane x-2y+z=6 and contains the line (x,y,z) = (2,-1,-1) + t(3,1,2).
The normal to the given plane, (1, -2, 1) lies in the plane to be determined. Another vector that lies in the plane to be determined is (3, 1, 2)
The cross product of the two is
`(1, -2, 1)ox(3, 1, 2)` = (-5, 1, 7)
The normal to the required plane is (-5, 1, 7)
If we equate t = 1, we get a point on the plane as (5, 0, 1)
Any vector (x - 5, y , z - 1) is perpendicular to (-5, 1, 7). The dot product of perpendicular vectors is 0.
=> -5(x - 5) + y + 7(z - 1) = 0
=> -5x + 25 + y + 7z - 7 = 0
=> 5x - y - 7z = 18
The required plane is 5x - y - 7z = 18
Related Questions
- Determine the cartesian equation of the plane that passes through the points (1,4,5) and (3,2,1)...
- 1 Educator Answer
- Vector reflection in a plane.Find the equation of the image of a line `(x,y,z) = (1,2,3) +...
- 1 Educator Answer
- Find a vector equation of the plane that is perpendicular tothe x-axis and contains the point...
- 1 Educator Answer
- Determine the Cartesian equation of a plane passing through the points A (3,0,1) and B(0,1,-1)...
- 1 Educator Answer
- A plane,`pi` has 3x-5z+3=0 as cartesian equation.Determine the Cartesian equation of plane that...
- 1 Educator Answer