Find the coordinates of the point K that lies along the directed line segment from J(4,1) to L(8,11) and partitions the segment in the ratio 3 to 1.

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

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

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Q: Find the directed distance from the given line to the given point. (-1, 6) (5, 4) (10, 8) (1, 2)…

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Q: Find 3xyd A A over the triangular region D with vertices (0, 0) (2, 0), (0, 4)

A: Given ∫∫3xy dA Over region (0,0)(2,0)(0,4)

Q: If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the…

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Q: Let →a=⟨3,1⟩ and →b=⟨1,0⟩. Find the projection of →b onto →a. proj→a →b=

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Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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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: Find –3xyd A over the D triangular region D with vertices (0, 0) (2, 0), (0, 4)

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Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: Let C be the oriented line segment starting at (0,0) and ending at (1,2). Calculate Sa F .n ds,…

A: To calculate the below line integral. ∫CF⋅nds Here Fx,y=y,−x C be the oriented line segment…

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

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

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Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: graph the points z = x + iy that satisfy the givenconditions.a. | z | = 2 b. | z | < 2 c. | z |…

A: a. We have given z=2 Then, put z=x+iy This implies that x+iy=2x2+y2=2x2+y2=4 Therefore, x2+y2=4…

Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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Q: 2. Find the images of the mapping W= z2 of the line y = 2.

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Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: Let p(x) =-2x* + c,x' + c,x + c,x + c, x ER be a polynomium whose graph insersects the points (-2,…

A: Given. We are given a fourth degree polynomial and also four points on the curve of the polynomial…

Q: Let l1, l2, and lz be nonconcurrent lines. Prove that there exist three points, exactly one each…

A: Given l1, l2, l3, three non cocurrent lines. the following cases are possible:  Case1: All lines are…

Q: Use Green's theorem to find $ x? ydr + xdy over a counterclockwise triangular path passing though…

A: To find the line integral ∮x2ydx+xdy by using Green's theorem, First, we need to draw the given…

Q: Find the locus of the points P(x, y) such that PA = 2PB where A is the point with coordinates (0, 3)…

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Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: Let, T:R' → R';T(x,y,z) = (x + y+ z,2y+z,2y+3z) 2. Find the dimension of KerT and ImT

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Q: If the plane F contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), L O 1 6 -6 O -2

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Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: 11. Given the coordinates X(0,0), Y(6,3) 0/4 and Z(2,1), find the ratio where point Z partitions the…

A: Use Section formula to solve this question. According to section formula: let coordinates of X is…

Q: Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .

A: GIVEN  Intersection with the xy-plane is the line r( t) = t ( 2, 1, 0)

Q: Show there is no plane perpendicular to n=i+jn=i+j that passes through points P(1,2,3)P(1,2,3) and…

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: tnd the kes reetor projection of anto r if

A: Given : u→=5i→+2j→ and v→=6i→-3j→

Q: Find the norm of the image of U(7, 8) by an reflection about y-axis Answer:

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Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: Let, T: R' → R';T(x, y,z) = (x+ y+ z,2y + z,2y +3z) Find the dimension of KerT and ImT

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Q: Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis,…

A: Let O is the initial point (0, 0, 0) and the vector OP, OQ and OR vector can be represented as:

Q: Prove that if P(I, y) be any point on the line segment joining R(11, Y1) and P2(12, Y2) then I= I1+…

A: Let P divides P1 and P2 in the ratio k : (1-k) x=kx2+1-kx1k+1-kx=kx2+x1-kx1x=x1+kx2-x1 Similarly…

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 the image of |z + pi + 2p| = 4 under the mapping w = p√² (e¹²) z. about

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

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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: If a = i + j + 5k and b = i + j + 3k, compute the cross product aXb

A: We have to find cross product

Q: Find ff 3xydA over the triangular region D with vertices (0,0) (2,0), (0, 4)

A: We will solve the problem

Q: Find the image of | z – 3i | = 3 under the mapping W =-.

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Q: Give a planar drawing of K2.3 with partition ({v1, v2}, {w1, W2, W3}).

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Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

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Q: Find the norm of the image of U(7, 8) by an reflection about y-axis

A: To Determine :-  The norm of the image of U 7 , 8 by an reflection about y- axis.

Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

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