B) Find the root and the height of (T, vo) where A = {1,2, 3, 4, 5, 6} and T = {(1,4), (3, 2), (2, 1), (1, 5), (2, 6)} (Show yo %3D %3D worl)

Q: A shop sells 3 brands of textile: B1, B2, and B3 of yarn, each of which is a blend of Orange (0),…

A: Given that,A shop sells 3 brands of textiles: B1, B2, and B3 of yarn, each of which is a blend of…

Q: Find an equation for the plane in R³ spanned by the points (1,5,

A:

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

A:

Q: Using the least square method, derive the following formulae for linear regressi model. Ex, Exy, -…

A: Let us start solving the problem and find a0,a1

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find symmetric equations for the line of intersection of the planes. 2 3x - y - 7, 2- Sx + 2y - 8 O…

A: Given:- Planes 1 z= 3x-y-z-7 Plane 2 z=5x+2y-8 To find:- Find symmetric equations for the line of…

Q: ear equation of the plane through the nts (6, 3, 2) and (4, −1, 1).

A:

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

A:

Q: F = (-3y, 3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 2).

A:

Q: Find an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: (a) the area of the triangle ABC where A(-2, -1,1), B(3, –2, 1) and C(1,3, –2). x +1 (b) the…

A: 3d

Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

A:

Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

A:

Q: JK in the coordinate plane has endpoints with coordinates (-4,11) and (8, -1). Find all possible…

A:

Q: 11) The distance from the point S(7, 6, -8) to the line x = −2 + 4t, y = -9 + 3t, z = 3 + 12t 12)…

A: #11) Given: Point = S7, 6, -8 and the line x=-2+4t, y=-9+3t, z=3+12t. To find: We have to find the…

Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

A:

Q: Find the equation of the plane con taining the points Р(4, -1, 3) Q(1, -2, -1) and R(1, 0, 8)

A:

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: = 8. = 8. 18) Area of a rectangle with base = x and height = y Area of a rhombus with one diagonal…

A: Area of rectangle with base x and height y is given by  Area =base ×height =xy

Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: 1. y = x², x = 0 , x = 2, y = 0, about the x – axis - 2. V9 - y?, у %3 1, у %3 3, а %3D 0, about the…

A: Use formula to calculate volume

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

A: The condition is z = −5

Q: 12 Which point is equidistant from the planes T1:- 2x +y- 2z + 3 = 0 and 73: - 2x + y- 2z + 21 = 0?…

A: Option B is correct :- (explained below)

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

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

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: 2. Find the equation of the plane through the points (1,–3,2), (3,0,–1), and (0,5,5).

A: The solution is given as follows

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: Line AB 100 mm long is 30 degree and 45degree inclined to HP & VP respectively. End A is 10 mm above…

A: Steps to find HT: Draw xy, one projector and locate VT on it. Draw locus of a110 mm above xy. Take…

Q: Q2. Find the vertices of unit square after shearing it along y-axis by a factor 2 and then…

A: Consider the unit square with vertices O0, 0, A1, 0, B1,1, C0, 1 as shown below:

Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 0, 1), and R(1, 1, 0).

A:

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Plot the points on the same three-dimensional coordinate system. (a) (3, 4, 1) (b) (-2, 3, 7) 10. O…

A: Given Data: Plot the points on the same three dimensional coordinate system. (a) (3,4,1) (b)…

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: a) Find the equation of the plane th

A: The question is taken from the plane in which we have to find the equation of the plane and integral…

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

A:

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: I need help w/ following integration by pullback

A: Given that R be the parallelogram with the vertices at (1,0), (3,1), (4,4), (2,3). And…

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

A:

Q: Find the centroid of the triangle whose vertices are  O(0,0) , A(4,0) and B(0,6)

A:

Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: Given U(1,3), V(-4,-4), and W(-3,6) on the coordinate plane, perform a dilation of A UVW from center…

A: