1. We can describe the location of a point in the plane using systems. The point P shown in ) and polar different the figure has rectangular coordinates ( coordinates ( •P

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: 10) Find an equation for the plane through Po(0,2,0)perpendicular ton = 31 – k.

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Q: Consider three points in three-dimensional space: ?=(11,2,−3),?=(2,−3,11),?=(−3,11,2) Let ? be the…

A: Let us consider the given points be To find the equation of plane containing the points A, B and C.…

Q: On a plane equipped with a polar coordinate system, what is the area of ​​the triangle with vertices…

A: In polar coordinate system x=rcosθy=rsinθ

Q: Exercise 7 Given the points A (-1;-1;1), B (-2; 0;0), C (-4; -1; 4) and D (0; 1;2). 1. Are the…

A: as per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: 6. [8.5] Consider the points A(1, 3, 1), B (2, 1, 0), and C(5, 1, 1). Determine the Cartesian…

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Q: Use Green's Theorem to calculate ( - sen(a))da + (2a + 3)dy, where C is the triangle with vertices…

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Q: Consider the hyperboliode H defined by the equation:  x^2+y^2−z^2=1 and the point P0=(1,4,4) in H.…

A: We are given the following hyperboloid : x2 + y2 - z2 = 1 And we have to choose the correct…

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: 1. Point L is a centroid of the triangle FWD. If RL = 54 cm, what is RD? W R ) 81 cm 58 cm O 100 cm…

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Q: Question # 4: Let and y = For what value(s) of h, is y in the plane generated by vi and va?

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Q: Example 7: Determine whether the planes x- 3y + 6z = 4 and 5x+ y - z = 4 are orthogonal, parallel,…

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Q: Considering only the 4-point planes that are drawn in the figure below, which point does NOT share a…

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Q: Question 1: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1,…

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Q: Let a point P has Cartesian coordinates 3 37 2 27 23 If (a, b, c) are spherical coordinates of P…

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Q: Question 4: A plane parallel to y-axis passing through line of intersection of planes x + y + z = 1…

A: A plane parallel to y-axis passing through line of intersection of planes  x + y + z = 1 and 2x + 3y…

Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: Points A and B are known to lie in a plane. a. What can you say about AB? b. State the postulate…

A: Solution: Consider the given that A and B are two points in any plane  (a) According to the…

Q: 20) Find two sets f polar coordinetes, (r, o),0LOL2 IT Por the point (6,6) in recten- gular…

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Q: 21. Find the equation of the perpendicular bisector of the segment joining (1,2) and (5,4) (Figure…

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Q: Given that all three points (6, 10, 10), (11, 14, 13), and (k, 8, 6) lie on a plane that contains…

A: If three points lie on the same plane then determinate of matrix made by that points is zero.…

Q: B) Use the diagram below to identify points, lines, and the plane. 1) List three collinear points.…

A: Given question:-  use the diagram below to identify points

Q: 4) Name a point that is coplanar with A, B, and C. b. E D a. D d. N C. F 3)

A: the given figure we have to name a point that is coplanar with A, B and C.

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: Consider a circle C in the xy-plane. If it is given that the points (2, 3),(2, −1) and (0, 3) are on…

A: Given points are (2, 3),(2, −1) and (0, 3)

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Find the coordinates of the vertices of the polygon after the given translation to a new position in…

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Q: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer.…

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Q: 2. Sketch a graph of the set of points which satisfy the following conditions. The coordinate…

A: In rectangular co-ordinate system:x= 2, is a yz-plane passing through x= 2.

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: Points in space should be given: A(1,1,0)  B(1,2,1)  C(-3,-4,2).  Calculate the coordinates of that…

A: We are given 3 points on a plane π such as A(1,1,0)  B(1,2,1)  C(-3,-4,2).  We need to find out the…

Q: D. Let ABCD be a trapezoid with AB parallel to CD. Let the lines containing the legs AD and BC…

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Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, z…

A: given

Q: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

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Q: Find the equations of planes passing through point (a,0,0) if these planes intersect one-sheet…

A: As per the question we have to find the plane which is tangential to the surface of the hyperboloid…

Q: Example 6: Determine whether the planes 3x+ y- 4z = 3 and -9x-3y+12z= 4 are | orthogonal, parallel,…

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Q: Given the points M(0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (C) the scalar…

A: We have to find the scalar projection and angle between vector.

Q: The standard equation of the sphere that has center (1,-2,1) and passing through the origin, is…

A: To find the standard equation of the sphere that has center 1, -2, 1 and passing through the origin.…

Q: 8. If the vertices of a triangle are A(8, 5), B(-1, 8) and C(2, -1) where would the centroid (Center…

A: Consider the vertices of a triangle is (x, y). The vertices of a triangle are: A(8, 5), B(-1, 8) and…

Q: Question 1: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1,…

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Q: m 5. Name four non-coplanar points. 6. What is the intersection of line m and plane P ? 7. Are…

A: To answer the questions related to given figure.

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: The general equation of the plane that contains the points (1, 0, 3), (-1,1,-3), and the origin is…

A: Explanation: Given that,  equation of plane ax+by+cz=0and (1,0,3), (-1,1,-3) and (0,0,0) on the…

Q: Two automobiles are driving on a plane. The first automobile is moving north at 10 m/s and rising 5…

A: Let's consider North as +ve y-axis, East as +ve x-axis, and upward motion to be +ve z-axis. Now, the…

Q: A plane meets the coordinate axes in A, B, C. If the centroid of aAl Show that the equation of the…

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Q: Question 22 Consider the plane T:r-z= 1 and the line 2 3 + -1. Find the equation of the plane that…

A: Solved below

Q: Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (1) What is the equation of the sphere…

A: Answer