C. Given the point C you found in part B, state the point symmetric to C about the y-axis. 24. Let A = (2,1) and B = (-1,–2) be two points on the plane. Write the equ~tion of the line which passes through the midpoint of A and B, and is perpendicular to the lin and B. Show work. ssing through A

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

A:

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

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

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: what is the equation of the plane parallel to the xy-plane and passing through the point  P0=(1    0…

A: We can write the equation of plane in general form and satisfies by given point

Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

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

A:

Q: You are given the following points: A=(−9,−11,19), B=(20,0,−4),C=(10,−11,−23). Which point is…

A: We need to find distance.

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: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: When the plane x = 3 passes through the surface x² + y? + 2? = 64, the curve that forms from…

A: Given, the plane x = 3 passes through the surface x2 + y2 + z2 = 64 . The intersection of plane x =…

Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

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

A:

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: b) Obtain the equation of a plane, P that is orthogonal to the line L:x=1+4, y=8+1, z =9+9t_and goes…

A: Given line is                                       L1:x=1+4t, y=8+t, z=9+9tvector parallel to line…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Find the equation for the plane through Po(6, – 3,7) perpendicular to the following line. x= 6+t, y…

A: Given equation of the lines are, x=6+t, y=-3-5t, z=5t The given equation of the lines can be written…

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

A:

Q: a) Sketch (hand drawn) the intersection of y? + z² = 25 and x = 3 in 3D. b) Also, describe the the…

A: When two surfaces intersect each other, a new curve is formed. The curve is referred to as the curve…

Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

A:

Q: 7, the line (X3+at.. y=26. Zo 5X-2y+42=10 at Zot).intersects. the paint p. Find the. coordinates…

A:

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

A:

Q: e. The plane through Po(2, 4, 5) perpendicular to the line x = 5+ t, y = 1 + 31, z = 4t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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 on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and…

A: The equation of the plane is

Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

A:

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 Point OF 3x +y+22 = 45 and the Line witth plaremetre eg dartons 1 = 1+t, y= 3 +2 € ,…

A:

Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: Find the distance, d, between the point S(5,6,5) and the plane 6x + 7y + 1z = 12. The distance, d,…

A: topic- distance between point and plane shortest distance of plane ax+by+cz+d from point…

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

A:

Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: Consider the following. 10z Sketch a graph of the plane. 10, 10. 10 10 10 10 10 10 10 10 Label any…

A: For a plane f(x,y,z)=0 For x intercept we have to put y,z=0 and solve for x For y intercept we have…

Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

A:

Q: Find the point on the plane 5x +4y+z 12 that is nearest to (2,0,1). What are the values of x, y, and…

A: The plane 5x+4y+z=12Normal vecor of the plane               <5, 4, 1>The point we seek would…

Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

A:

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: is cut by the plane given by y = the point (1, 3, -8). 3x, producing a curve in the plane. Find the…

A:

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

A:

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A:

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

A: ee

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

A:

Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

A:

Q: Find the distance, d, between the point S(9,3,5) and the plane 9x + 1y + 1z= 36. The distance, d,…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…