The area of the triangle with vertices V141 P (1, 5, 2), Q (0, 0, 0), R (3, 5, 1) is

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: The vertices of a square are H(0, 2), I(2, 0), J(0, - 2) and K(-2, 0).

A: Transformation of a function: A function transformation takes whatever the fundamental function f…

Q: Evaluate the line integral along the given path(s).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: The triangle abc (in UHG-universal hyperbolic geometry) is equilateral, i.e., the quadrances are all…

A: Given that, The triangle abc (in UHG-universal hyperbolic geometry) is equilateral, i.e., the…

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

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Q: What is the vertex of y = Vx + 4+1 O (4, -1) O (4, 1) O (-4, 1) O (-4, -1)

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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: A quadrilateral has the following vertices given: P1(1,4),P2(3,4),P3(3,6),P4(1,6).the coordinates…

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

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Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: Find b and c so that y = – 5z² + bz + c has vertex (9, 1). c =

A: The given equation y=-5x2+bx+c has a vertex at (9, 1). The given equation is an equation of a…

Q: Find the perimeter of the triangle whose vertices are the following specified points in the plane.…

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Q: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: The area of parallelogram whose adjacent sides are i^-2j^+3k^ and 2i^+j^-4k^ is

A: Given sides arei^-2j^+3k^  &  2i^+j^-4k^

Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 5. Rhombus CDEF with vertices C-5, 5), D(-1,7), E(-3, 3), and F(-7, 1): 270° counterclockwise E D:…

A: When rotating a point 270 degrees counter clockwise  about origin, point x,y becomes y,-x. This…

Q: 2. Triangle ABC with vertices A(0, 7). B(7, 3). and C(1, 4): (x, y)→ (x- 3, y – 4)

A:

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Find the area of the triangle P QR with vertices P (1, 1, 0), Q(7, 1, 0) and R(9, 4, 2). (Your work…

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Q: 1)calculate xy dady Where D is a triangle with vertices (0,0), (5,0) and (5,5) tip:Don't use the…

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Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: Find the area of the triangle with vertices P(1, 0, 7), Q(0, 6, 7), and R(1, 4, 0).

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

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Q: 2. Triangle VWX with vertices -1, 0), W6, 8), and X(4,-3): (x, y) (x-1, y-5)

A: Given coordinates V(-1,0)W(6,8)X(4,-3)Given transformation :(x,y)→(x-1,y-5)

Q: The area of the triangle with vertices at P = (1, 0, -2), Q = (2, 3, 1) and R = (2,1,0) is O a) V14…

A:

Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O…

A: topic - shortest distance between point and sphere

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Consider a rectangular box below A (2,3, 5) 1.2 Find the length of the diagonal of the box…

A: O= (0,0,0) A=(2,3,5)

Q: The wedge cut from the cylinder, x2 + y? =1 by the planes, z = -y and z = 0. Set up only

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Q: The triangle abc (in UHG-universal hyperbolic geometry) is equilateral, i.e., the quadrances are all…

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Q: Find the projections of a regular hexagonal pyramid given by the axis o(M[-40,15,30],N[5,45,45]),…

A: Edge of base =20 {mm}Axis length =40 {mm}Resting on one of its triangular face on (Ground) HPEdge of…

Q: 5.) Find the area of the triangle whose vertices are at A (-2,3), B (6, -6), C (8,0)

A:

Q: *15. What is the name for the point on the coordinate plane that has the (Inv. 7) coordinates (0,…

A: The given point is: (0, 0)

Q: show that points (2) ) are ( 3 ) 2 (52) A on-Coplaner ( ره ) -

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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find all values of x so that the triangle with vertices A=(-2, –1, x), B=(-4, -2, –2), and C=(-2,…

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Q: Find the point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

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Q: 8 If the shaded square has center at C and an area of A, find C and A. 'y-axis C• (-4, 0) (0, 0)…

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Q: Quadrilateral PQRS has vertices P(-4, 2), Q(0, 8), R(3, 6) and S(-1,0). Prove that PQRS is a…

A: join all coordinates  Properties of Rectangle: Opposite sides are equal and its diagonal are equal.

Q: Square QRST has two vertices at Q(-9, 5) and R(-7, 7). Which could be the coordinate of the vertex…

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Q: Consider the triangular region in the plane given by the triangle (1, 6), (6, -1), and (1, -4).…

A: See attached file for a step by step explanation.

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: 9. Square ABCD with vertices A(-7, 5). B(-4, 7), C(-2, 4). and D(-5, 2): 90° counterclockwise

A: To graph the square with given points A,B,C,D.

Q: Find the area of the triangle with the given vertices. (Hint: 1lu x v|| A(0, 0, 0), B(1, 0, 3),…

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