Check that the point (1,-1,2) lies on the given surface. Then, viewing the surface as a level surface for a function f(a, y, z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1,-1, 2). vector normal = tangent plane: 4x² - y² + 3z² = 15

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: x + y+ 3z = 0 x-y-z%3D0 2. Find the included angle between the line and the planex -y-z+1 0.

A: we have equation of lines:    x+y+3z=0..... (i)-x+y+z=0..... (ii)Add equation (i) and…

Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Q4\A: Find area of zone bounded by curves x = y? 2y = x-3 B: Find area of triangle whose vectors…

A:

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

A:

Q: KnOwn equation x² + y² + z-9 = 0 and a point X₁(1,2,4), Determine: a. tangent vector equation; b.…

A:

Q: Find an equation of the tangent plane to the surface at the given point. X²+y²+z²=14, (1,2,3) And…

A:

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

A: