Find the point on the plane x+ 2y - z 12 that is nearest the origin.

Q: Find the equation of the plane which passes through O and is parallel to z – (5x + 6y) = 3 x+ y + z…

A: see 2nd step.

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

A:

Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

A:

Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

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

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

A:

Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

A:

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

A:

Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

A:

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

A:

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

A:

Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

A:

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.

A:

Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A:

Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

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: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

A:

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: Find the point p(x, y, z) on the plane 2x + y - z - 5 = 0 that is closest to the origin.

A: Given:The given plane is 2x+y-z-5=0 that is closest to the origin.To find:we have to find…

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

Q: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

A:

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

A:

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: The line L(t) = (2+1,8-31, 2t-6) intersects the plane 2y - 3x + 3z = -11 at the point

A: Given, the line             Lt=2+t, 8-3t, 2t-6                                   ...(1) Intersects…

Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

A:

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

A: Here we have to find the point at which the line x=2, y=3+2t, z=-2-2t meets the plane 6x+3y-4z=-12…

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

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: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

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 equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane