· Let A the area of the triangle ABC is given by ("1, ул), В %3D (x2, Y2), and C = (x3, y3) be distinct points on the plane. Show that %3D X1 Y1 1 1 det | x2 areaABC = Y2 1 | x3 Y3 1

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: 2. The x- and y-axes divide the coordinate plane into four regions called

A: Given: The x and y axes divide the coordinate plane into four regions

Q: What is the sketch the phrase "three collinear points and a fourth point not on the line of the…

A: Introduction: Dual of any phrase can be find by replacing the conjunction connective with…

Q: Points X(6, 8), Y(3, 3), and Z(13, -3) form a triangle. What is the area of AXYZ? area of AXYZ =

A: If P(x1,y1),Q(x2,y2) and R(x3,y3) are the points of the triangle , then                Area of the…

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: For parts (a), (b), and (c) consider the solid that lies above x +y -z =0 and below by x² + y* +z…

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Q: Two sides of a square lie on the lines x + y = 1 and x + y + 2 = 0. What is its area?

A:

Q: In parallelogram WXYZ, diagonals WY and XZ intersect at point A. Give WA = x^2 - 48 and AY = x^2 -…

A: We have to find WY

Q: 9. Plot these three coordinate points on the given Cartesian Plane: (2,3) (-2,1) (4,-1) Join the…

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Q: 2. Let ~v = h3,-2,1i and w = h-1,4,2i. (a) Find cos(0) where 0 is the angle betwen ~v and w.

A: Given,   v→=3,-2,1 and w→=-1,4,2

Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the area of the triangle UVW

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