). Find a parametric representation for the line of intersection of the following two planes: I - y + z = 0, 2x + 5y - : = 1.

Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Consider the following. 3x + 3y + 7z = 63 Sketch a graph of the plane.

A: 3x+3y+7z=63 x intercept = (21,0,0) 3x+3*0+7*0=63 3x=63 x=21 y intercept = (0, 21,0) 3*0+3*y+7*0=63…

Q: Is the set c~(R* U {0}) “the entire plane without the non-negative reals" conformally equivalent to…

A: We need to evaluate the statement "the entire plane without non negative reals, ℂ-{ℝ∪{0}}, is…

Q: Consider the planes II : 3z – y+ 2z=1, Il2 : -9z + 3y – 6z = 24 and the line of parametric equations…

A:

Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: osen y

A: Is it sen y =x

Q: If S is projected onto the x – y plane, what is the shape of the resulting projection?

A: Idea: if we project the surface in xy- plane z=0. if we substitute z=0 in surface equation we get…

Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: Let L1 be the line through the points P(1,0,2) and Q(2,1, 1), and L2 be the line defined by the…

A: Given- Let L1 be the line through the points P1, 0, 2 and Q2, 1, 1, and L2 be the line defined by…

Q: Let W1, W2 be planes in 3-space defined by equations W1 :¤1 – 2x2 + 3x3 = 2, W2 : x1 – x2 + 4x3 = 3.…

A:

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

A:

Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Let's solve.

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: Which of the following shapes could tessellate a plane on their own?

A: We know that triangles, squares and hexagons are the only regular shapes which tessellate by…

Q: Which of the shapes below can make a regular tessellation of the plane?

A: there are only three regular polygons for tessellation and they are equilateral triangle, square and…

Q: describe the given set in spherical coordinates  y2 + z2 ≤ 4, x = 0

A: y2+z2≤4,  x=0. Now consider, y2+z2≤4⇒x2+y2+z2≤4+x2⇒x2+y2+z2≤4             ∵x=0⇒ρ2≤4⇒0≤ρ≤2 Now since…

Q: Let r() = (In1, 1, 5). Find the equation of the osculating plane corresponding to1 = 1.

A: Find the point at t=1 the vector r(t)=lnt,t,t22 corresponds. lnt,t,t22=ln1,1,122=0,1,12=0,1,0.5…

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

A:

Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Prove that the locus of the foot of the perpendicular drawn x2 +² a? = 1 to any of its tangent om…

A:

Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

A:

Q: Let W1, W2 be planes in 3-space defined by equations W1 : 21 – 2x2+ 3x3 = 2, W2 : x1 – x2+ 4x3 = 3.…

A:

Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

A:

Q: Find a set of parametric equations for the curve of intersection of the given paraboloid and plane:…

A: Solution:-

Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

Q: Write down the parametric equetions |3D 4=6-t in cartesion Form

A:

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A:

Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.

A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…

Q: Derive the formula for the distance between points P1(p1,q1,z1) and P2(p2,q2,z2) given in spherical…

A:

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: QUESTION 1 For the parametric line L: x =4+t, y y =3+t, z=D3+2t and the plane P: -y = x+ 2z + 2,…

A: Compute the direction ratios of both the line and the normal of plane.

Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

A:

Q: Find a parametrization c(θ) of the unit circle such that c(0) = (−1, 0).

A:

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: Find a parametric representation for the surface: The plane through the origin that contains the…

A:

Q: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec θ

A:

Q: Which of the following graphical representations shows the intersection curve, in the first octant,…

A: We have to choose which one shows the intersection curve in first octant between a cylinder of…

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

A:

Q: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…

A:

Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a)…

A:

Q: Find a plane containing t and orthogonal to the pla

A:

Q: Given, (2z - z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)?…

A: Given integral ∫Γ2z-z¯dz where Γ is the line segment from -i to 1. i.e., it is a line segment from…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Consider the planes 2x − 3y + z = 6 and −2x + 4y − 3z = 4 Find parametric equations x(t), y(t), z(t)…

A: Given :-  The given planes are : 2x -3y + z = 6-2x + 4y -3z = 4 To Determine :-  The Parametric…

Q: Give two parametric representations for the plane curve. 1. y#-4 y + 64 %3D

A: