You are given the following points: A=(−9,−11,19), B=(20,0,−4),C=(10,−11,−23). Which point is closest to the yz-plane?       What is the distance from the yz-plane to this point?  Which point is farthest from the xy-plane?       What is the distance from the xy-plane to this point?  Which point lies on the xz-plane?

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: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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Q: Find the equation of the plane through (1,-4,2) and per pendicular to each of the planes 2x t 5y -2…

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Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: Find the x-, y-, and z-intercepts of the plane. (If an answer does not exist, enter Di 4x - 5y + 2z…

A: for x intercept, y=z=0 for y intercept, x=z=0 for z intercept, x=y=0

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: What is the y-coordinate of any point in the xz-plane?

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Q: Find the equation for the plane through Po(7.- 3. - 1) perpendicular to the following line. x=7+t,…

A: Ans     equation  of  line          x=7+t,   y=-3-3t,  z=-2t  or   x-71=y+3-3=z+0-2

Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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Q: Find the coordinates of the point that is located nine units in front of the yz-plane, six units to…

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Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: 1 2x 3y + z = 0 and 2 +t - 1 1

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Q: By setting one variable constant, find a plane that intersects the graph of z=9x^2−3y^2+1 in a:…

A: Given that -  z=9x^2−3y^2+1

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: You are given the following points: A =(-4,7,20), B = (-16,0, 3), C = (5, 2, -21). Which point is…

A: Use distance concept from plane

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: You are given the following points: A = (11, –14, –16), B = (16,0, 5), C = (-9, 16, 13). Which point…

A: Answer

Q: Find the distance between the points A(-5, -6, 2) and the plane that includes the y-axis and the…

A: As per Bartleby guidelines rule I am answering only first question as both question is not a…

Q: You are given the following points: A = (11,20, –-18), B= (19,0,3), C =(-7,10,14). Which point is…

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Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

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Q: The distance from (-3,-4,-7) to the yz-plane is (A) -4 (B) 4 (C) -3 (D) 3 (E) 7

A: The distance(d) between two points (x1,y1,z1) and (x2,y2,z2) in a cartesian coordinate system is…

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

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Q: The distance from (-2,-5,-6) to the yz-plane is (A) -2 (B) 2 (C) (D) -5 (E) 6

A: Use distance between two points

Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: Find an equation of the plane containing the points P(O,0,o) and Q(2,2,2) and parallel the line…

A: Given:- Equation of line x= t, y = 1,z= t  To find:- An equation of the plane containing the points…

Q: Which of the points A(-4, 0, -1). B(3, 1, -1), and C(2, 4, 6) is closest to the yz-plane? Which…

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Q: Find the equation for the plane through Po(-2, -7,- 4) perpendicular to the following line. x= -2-t,…

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Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: You are given the following points: A = (-4, 5, 16), B = (-17,0, 3), C = (5, –6, – 20). Which point…

A: 3D coordinate

Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: You are given the following points: A = (-4, 20, 16), B = (20, 0, 7), C = (8, –15, – 19). %3D Which…

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

Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

Q: The point is located in the yz-plane, three units to the right of the xz-plane, and two units above…

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Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z = x+ y. Leave…

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Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: Find the equation for the plane through Po(4,- 5,5) perpendicular to the following line. x= 4 + t, y…

A: ee

Q: Find the distance from the point (7,-9,-5) to the plane 3x + 5y = 51.

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Q: Find the equation for the plane through Po(-6,9,2) perpendicular to the following line. x = - 6 + t,…

A: Given that the point is P0(-6, 9, 2) and perpendicular line: x = -6 + t, y = 9 - 5t, z = 4t