Type the coordinates of the images P', Q', and R' for each of the following points under the translation defined by (x,y)→(x+5,y- 4). a) P(0,0) b) Q(- 3,5) c) R(- 7,- 2)

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Find the projection of d on the plane P if a 4 and P has the equation x + y+ z = 1.

A:

Q: Find the coordinates of W. When point W lies on UV such that UV:VW is 5:2

A:

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

A:

Q: An equation of a plane P passes through the point (0,0,-3) and perpendicular to the line L:x = 1-2t,…

A:

Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

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

A: We have to find the parametric form of directed line segment from -i  to 1

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

A:

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

A:

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

A:

Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

A:

Q: The parametric equation for the line passing through P(1,1,5) and parallel to n=(0,0,1) is defined…

A: Topic = Vector

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

A:

Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y – 2z…

A: Given:

Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

A:

Q: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point…

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point…

Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

A:

Q: find the line of intersection of th e given planes. 3x + 2y + z = -1 and 2x - y + 4z = 5

A:

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

A:

Q: Consider the projection from the origin of the straight line y + x = 2 on a straight line y + 2x =…

A: Graph formed by

Q: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

A:

Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

A:

Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

A:

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

A:

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy > 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A:

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

A: