Q5/ find the equalion of bhe plane that contains the Line: X- g+l=Z= andl the Point A(5,1,1) %3D %3D

Q: Q3:Find equation of the Plane determined by the inter Sectiny (X-5+2{ ツ=ー!+& そ=C+4) (x=3-t ッ= 6+z4,…

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Q: Q5/ find the equalion of bhe plane that Condains the Line: x-!= +!2= and the Point A(5,1,) %3D 2.

A: See the attachment

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: Find the point where the line x = 8/3+ 2t, y = -2t, z = 1 + t intersects the plane 3x + 2y + 6z = 6.

A:

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

A: Find the distance between the origin and plane containing the points A(1,1,0) , B(-1,0,1) and…

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

Q: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6?

A: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6? Given x, y, z in…

Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

A:

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.

A: We have to find the equation of plane .       According to our guidelines ,we cannot solve all…

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

A:

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

A:

Q: H.W: Find the point where the line 8 +2t, y= -2t , z= 1+t intersects the plane 3x + 2y +6z = 6

A: We have to find the point where the line x=83+2t, y=-2t, z=1+t intersects the plane 3x+2y+6z=6.

Q: Find the intersection of the line and the plane. x + y + z = 14, r(t) =〈1, 1, 0〉+ t〈0, 2, 4〉

A: Given that, The equation of the line is: x + y + z = 14 And, the equation of the plane is:  r(t)…

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

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Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

A:

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: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Find the point at which the line intersects the given plane. x = 2 − 2t,    y = 3t,    z = 1 + t;…

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

Q: Plot the portion of x² +2²=9 above the xy-plane and between y = 1 and y=5. Make sure you use the…

A: Any point on the three dimension can be represented by the coordinates: x, y, z.

Q: Q5/ fiud the equalion of bhe plane that Condains The Z-! and the Point A(5,\,') Line : う+! %3D %3D…

A: Equation of line is x-12=y+13=z-13Let equation of plane passing through (5, 1, 1) is a (x-5)+b…

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

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

Q: When the plane x = 3 passes through the surface x2 + y? + z² = 64, %3D the curve that forms from…

A:

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 the point where the line x=8+2t,y=-2t ,z=1+t intersects the plane 3x+2 y+6 z=6.

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

A:

Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets…

A: Given that the line is passing through origin so ro = (0,0,0) and perpendicular to the plane 2x – y…

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

A:

Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

A:

Q: Q5: Find the distance of the point (2. –2,1) from the line х-2 y-3 = z+2 2 4 3 measured parallel to…

A: we have to find the distance of the point (2,-2,1) from the line x-22=y-34=z+23 measured parallel to…

Q: Find the intersection of the line and the plane. 2x + y = 3, r(t) =〈2, -1, -1〉+ t〈1, 2, -4〉

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

Q: The line x=4+2t, y=-t, z=-1-4t is parallel to the plane 3x+2y+z=7 FO

A: Direction cosine vector of the line is: L=2,-1,-4 and normal vector to the plane is N=3,2,1.

Q: Find the point at which the line intersects the given plane. x = 3 - t,   y = 3 + t,   z = 2t x - y…

A: Substitute the line equation in the plane equation

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

A:

Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

A:

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 intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

A:

Q: Find the point P where the line L(t) = intersects the plane 2x + y − z = 16

A:

Q: H.W: Find the point where the line 8 x=+ 2t , y= -2t , = 1+t intersects the plane 3x + 2y +6z = 6

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

Q: find the point in which the line meets the plane x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

A:

Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: Find the distance between the parallel planes – 2x + y +z = 0 and 10r – 5y – 5z – 11 = 0. Note:…

A:

Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

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

Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Find the point at which the line meets the plane. x=3 + 3t, y = 4 + 5t, z = - 3+4t; x + y + z = 4…

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: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

A:

Q: find the point in which the line meets the plane x = 1 + 2t, y = 1 + 5t, z = 3t; x + y + z = 2

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

Q: Find the coordinates of the point where the line F= (1+21)i +t} – 2tk 2z - y+z= 1. intersects the…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.