# Calculus Grade 12

posted by .

Find the equation of the plane that passes through the point (3,7,-1) and is perpendicular to the line of intersection of the planes x-y-2z+3=0 and 3x-2y+z+5=0

• Calculus Grade 12 -

The line of intersection of the planes is in the direction of the cross-product of the two normals:

{1,-1,-2}x{3,-2,1} = {-5,-7,1}

Now we have a point and a normal vector.
The equation of the plane is thus

-5(x-3) - 7(y-7) + 1(z-1) = 0
-5x + 15 - 7y + 49 + z - 1 = 0
5x+7y-z = 63

## Similar Questions

1. ### calculus

find a vector equation of the line, which passes through the point (1,3,11) and is perpendicular to the yz-plane
2. ### Calculus

Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4
3. ### Calculus

Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4
4. ### precalc

I;m not sure if i am doing this right...I keep getting a negative intersection point, which doesn't seem possible. Please help! a) find the equatoin of line 1 which passes through (1,3) and (9,7) I get y=3+1/2(x+1)or y=1/2x+2.5 b) …
5. ### Calculus

Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the …
6. ### Linear Algebra

1. Considering 2 planes with equations: x + 2y - 3z = 1 x + 2y - 3z = 18 (a) Given (a,b,c) a point on the first plane, find the point where the line perpendicular to both planes passes by (a,b,c) and through the 2nd plane.
7. ### Linear Algebra

1. Considering 2 planes with equations: x + 2y - 3z = 1 x + 2y - 3z = 18 (a) Given (a,b,c) a point on the first plane, find the point where the line perpendicular to both planes passes by (a,b,c) and through the 2nd plane.
8. ### Calculus

Find an equation of the plane. The plane that passes through the point (−1, 2, 1)and contains the line of intersection of the planes x + y − z = 4 and 4x − y + 5z = 4
9. ### mathematics

Find the equation of a straight line which passes through the point P(3,1,-2) and is perpendicular to the planes L1 and L2, where L1 : x - 3y + 2z = 2, L2 : 2x + y - 2z = 5.
10. ### Calculus

Consider the line through the points (3,2,5) and (1,1,1). Consider the plane A that is perpendicular to this line, and passing through the point (-1,0,2). Consider the plane B that passes through the points (1,-1,0), (0,2,0), and (0,5,2). …

More Similar Questions