Trapezoid TRAP with vertices T(8,2), R(-5,8) A(-2,5) and P(-3,3): x axis's

Q: 4. Trapezoid JKLM with vertices J(2, 1) , K(5, 1), L ^ n * (8, - 4) and M(1,-4);90 ° clockwise…

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Q: The plane 7= [1,0,0]+t[1,1,1]+s[L,−1,1]; s,t €R contains the point (3,0, p). Find the value of p.

A: Given r=(1,0,0)+t(1,1,1)+s(1,-1,1)

Q: Rhombus WXYZ with vertices W(1, 5), X(6, 3),Y(1, 1), and Z(-4, 3) in the x-axis W'

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Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: Trapezoid PGRS with vertices P(-6, 2), G(-2 -0, R(-2 -3), and S(-6, -6), reflect in the linex-1 (4)…

A: We need to draw transformed image.

Q: 6. Quadrilateral STUV with vertices S(-4, 2), T(-2, 6), U(1,7), and V(4, 1) in the x-axis. nioM S'L.…

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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: 7. Rhombus FGHI with vertices F(6, -1), G(11, -3), H(13, -8), and I(8, -6): scale factor = 2,…

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Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: The plane through the point (3,-1,2) can perpendicular to the a) x-axis b) y-axis c) z-axis d) non d…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: In space coordinates system, the y-axis consists of all points of the form O (x, 0, 0) O (0, 0, z) O…

A: we know that(x,y,z) is nothing but distace of a point from origin along the x,y,z-axis

Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: 3. Line segment JK in the xy-coordinate plane has endpoints with coordinates (-4, 11) and (8, -1).…

A: As per guidelines we can answer only one question at a time, so the first question can be answered…

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: 2. Trapezoid QRST with vertices Q(3, 1). R(5. 2). S(10. 0). and 714, -3); 270° counterclockwise…

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Q: 3. Rhombus KLMN with vertices K(-3, 2), L(1, 4), M(-1,0), and N(-5, -2): (x, y) → (x, y- 5) 4. Re…

A: First we draw Rhombus KLMN and then Draw Rhombus K'L'M'N' .

Q: 4. Using two methods find the point point P = (5, 4, 4) on the plane x +y + z = 4 nearest the %3D

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Q: Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x −…

A: In this question, we need to find the curve which describes the intersection of the surfaces.…

Q: Find the point on the plane −2 x+y−z =−9 that is closest to the point (3,−2,2) .

A: We have to find a point on the plane closest to another point.

Q: having ita Ans. Centers: (2, 1), (1, 4). y = 3, 7x +y = 5, and having ita center or. 16. Touching…

A: Topic-circles

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: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: Find the shortest distance from the point (1, 0, -2) to the plane x + 2y + z = 16. The distance from…

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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: 4. Rhombus WXYZ with vertices W(-2, -4), X(1,-2), Y(4, -4), and Z(1,-6):x-axis W: Y: X': Z':

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Q: Find the points on the cone z 22 x2 + y? that are closest to the point (-5,2,0)

A: Find the points on the cone z² = x² + y2 that are closest to the point (-5,2,0).

Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

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Q: 5/ Find the point at which the line through points P1(2. 3, 0) and P2 (-6. -3, 12) meets the plane…

A: Consider the points  P12,3,0 and P2−6,−3,12

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: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

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Q: 7. For trapezoid WXYZ, U and V are midpbints of the-legs. Find UV. W x +7 8x-3 6X +5

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Q: B': 3. Trapezoid FGHI with verlices F(-5,-2), G(-2,-2), H(0, -6), and (-8,-6): y-axis F': H: G: I':

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Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: 5. Quadrilateral WXYZ with vertices W(0, -4), X(13, 0), Y(9, -12), and 2(5, -12); scale factor: k -…

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Q: Findauihtvectorhermat to thesuFace X Y +X2=1 et the Point (-1,1,1)

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Q: Use Lagrange multipliers to find the shortest distance from the point (7, 0, −9) to the plane x + y…

A: The square of distance function is given by fx,y,z=x-72+y2+z+92 and the constraint is…

Q: 2. Center: (2, -1) Focus: (2, -31) Vertex: (2, 23) (v+1)° ¸ (x-2)² [A] = 1 576 324 (y+1) _ (x-2)*.…

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Q: 3. 4. Circumscribing the triangle with vertices (a, U), (a, d), (U, %). 2a = 0. Ans. z2 + y+ ax- ay…

A: In the question we have to find equation of circle circumscribed in a triangle. NOTE - As per…

Q: Find the shortest distance from the point (2,0,–3) to the plane x + y + z = 1. . Use Lagrange…

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Q: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: 6. trapezoid DEFG with vertices D(0,-3), E(1, 3), F(3, 3), and G(4,-3) in the y-axis ty O X D' =_ E'…

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Q: Find a point with z = 2 on the intersection line of the planes x + y + 3z = 6 and x - y + z= 4 .…

A: Given, equation of planes x+y+3z=6x-y+z=4

Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

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Q: ind the equation of the parabora y= ax^2 +bx +c that passes through points (0,3) (1,-4) (-1,4)

A: Consider the equation of parabola is given as in the question and passing through the points (0, 3)…

Q: 3. Trapezoid JKLM with verlices J(-4, 3), K(-2, 7), L(2, 7), and M(3, 3): y- 1 K'C L'C M 111ו

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