. Find the equation of the line containing the point (1,3, –2) that is parallel to both of the planes x + 2y – z = 4 and 2x – y+ z = 1.

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: Find the point at which the line T(t) = (4, 1, 7) +t( – 5, – 7, – 4) intersects the yz plane.

A:

Q: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

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

A:

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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 a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: parallel

A:

Q: Find the point of intersection, if any, of the plane T: 4x + 2y – 2z=1 and the line l : 3 +t 1

A: Point of intersection of line and plane

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

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

A:

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

A:

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

A:

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

A:

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2)…

A:

Q: Show that the condition that the curves ax²+by²=1 a'x?+b'y²=1 1 1 1 1 Should intersect orthogonally…

A: If m1 = tangent at point (x,y) and     m2 = tangent at point (x,y) then Orthogonal conditions is…

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 an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t D)= O…

A:

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

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 shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Perpendicular to each of the planes x – z+ y = 0 and 2x + z – 4y = 5 and containing the point (4,…

A: We have to find an equation of the plane which is perpendicular to each of the planes x-z+y=0 and…

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

A:

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: х —7 у-5 z-1 L: 4 -,P: 2x + y – 7z +1 = 0 6. 3

A: Given Data: Line: x-74=y-53=z-16 Plane: 2x+y-7z+1=0 Let t is a constant variable for line,…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

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: Which of the following is an equation for the line through the point (2, 3) and perpendiçular to the…

A:

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: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

A:

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: 21. Determine an equation for the line of intersection of the following planes: 3x + 2y+ 5z = 4 and…

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: