Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4 af ду dg %3D (10,5) SO – (16x*y?dæ + 8yæ*dy) = - II

Q: A constant vector F = ai + bj is path independent.

A: Given vector F→=a i +b j

Q: Evaluate I = fe(sin z + 9y) dz + (7z + y) dy for the nonclosed path ABCD in the figure. А - (0,0),…

A: Given integral is I=∫Csinx+9ydx+7x+ydy For non-closed path, integration will be…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

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Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

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Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi-…

A: We have to the value of integral.

Q: S show. that the line in..which. the planes.X+.2y-2Z=5 and. 5X-zy..Z=0..jntersect..s..pavallel.o.…

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Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

Q: Find the line of intersection of the planes 2x – y+ 3z = 1 and -r + 3y + z = 4. Lütfen birini seçin:…

A: Given planes are 2x−y+3z=1 and −x+3y+z=4. We have to find the line of intersecting of the plane…

Q: Show that there are no points (x, y, z) satisfying 2x - 3y + z - 6 = 0 and lying on the line v = (8,…

A: Given line v is: v=8,-8,-4+t(1,1,1)  =(8+t,-8+t,-4+t) Therefore, if (x,y,z) lies on the line v, then…

Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

Q: 1. How can two pencils (representing lines) be held so that a plane can be passed containing both;…

A: Please submit parts 2 and 3 separately for them to be answered. For the first part, Two lines, in…

Q: Point A has coordinates of (9,7,4) and Point B has coordinates of (2,9,5). What is the x-component…

A: Given problem Given that   Point A has coordinates of (9,7,4) Point B has coordinates of (2,9,5)…

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: 3.2 Evaluate where z = x + iy with y the path on line from z = 2+i to z = 1 + 2i.

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Q: 2. Trapezoid QRST with vertices Q(3, 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

A: Rules for counterclockwise rotation about the origin: 90°  : x,y →-y,x180°: x,y →-x,-y270°: x,y…

Q: 3. Prove by the analysis of orthogonal trajectory that the lines Ax + By = C and Bx – Ay = k are…

A: let slope of line Ax+By=C is m1By=-Ax+Cy=-ABx+Cso m1=-ABslope of line Bx-Ay=k is m2Ay=Bx-kso…

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

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Q: Suggest a "vector proof" of the fact that, inR2, two lines with slopes m1and m2 are perpendicular if…

A: Given: ℝ2 To Prove that : m1 m2=-1

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

A:

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: Find the Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

Q: 2. Trapezoid QRST with vertices Q(3. 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

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Q: Show that there is no hamiltonian path in Cay ({(1,0),(0,1)}: Z3 +Z2) from (0,0) to (2,0

A: Given problem is : Show that there is no hamiltonian path in Cay ({(1,0),(0,1)}: Z3 +Z2) from (0,0)…

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: Let C be the straight line path from (0, 1, 2) to (2,0, 5). 1. Compute ſo ry ds. 2. Compute fc x dr…

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Q: Show that there are point(s) (x, y, z) satisfying 2x − 3y + z − 5 = 0and lying on the line v = (5,…

A: The given equation of the line is

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the…

A: A given set of points can be assumed to be on a surface given by an equation when the each of…

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

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Q: The line of intersection of the planes 2x +y - z= 4 and 4x – y+3z = 2 has equation %3D O a) (x, y,…

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Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Verify the chain rule for jacobian, if y2 u = x + , v = * y2 %3D

A:

Q: Show that Si2 f dæ + g dy + h dz = S - (4xy³z*dx + 6y?x?z4dy + 8z°y³x²dz) is independent of path:…

A: