8. Provide a rough sketch of the surface in R³ : (a) defined by 3x² − 12x − y + 2x² + 4z + 9 = 0. Justify your work. - (b) which consists of those points (x, y, z) € R³ which satisfy x x - x (4,2,-2) ≤ 3, where x is the position vector (x, y, z). Justify your work.

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

A:

Q: 32²+62-4x-3y+2=0. 1. identify the surface: Present a well-defined sketch of the surface.

A: Given, the surface               2x2-3z2+6z-4x-3y+2=0

Q: I need help with 3 and 4 only. I think I figured out 1and 2.

A: Step 1:  q3)  r(u,v) = <u, v, u+v-4> Here, x= u,y=v,z=u+v-4 =x+y-4 Or x+y-z= 4 This is the…

Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: Consider the surface of equation z = x2 + y² . What is the equation for the tangent line to S at the…

A: We need to find equation of tangent line.

Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

A:

Q: classify and sketch the surface given by x2+2y2+z2-4x+4y-2z+3=0 (indicate the vertex coordinate)

A: Here we have given a surface equation as below:  x2+2y2+z2-4x+4y-2z+3=0 The surface given by the…

Q: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Describe and sketch the surface given by the function.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

A:

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

A:

Q: Sketch the surface of f(x,y)

A: To sketch the function

Q: Consider the equation 4y^2 + z^2 − 4x − 8y + 4z + 8 = 0. Then classify the surface it represents…

A: Given equation of surfaces 4y2+z2-4x-8y+4z+8=0

Q: y² - (z²/3) = 1 + (x²/12) sketch the quadric surface. emphasize the traces on the coordinate planes…

A: Given a quadric surface y2-z23=1+x212. YZ trace: When x=0, we get y2-z23=1. This is a hyperbola on…

Q: arameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.

A: To parameterize the intersection of the plane x = 1 and the surfacez=x2−2x2y+y2, we can set x = 1 in…

Q: 32. 3. 24 (a) y - x - = 1 (b) y + x - z = 1

A: Hyoerboloid

Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

A: