Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find the equations of the Line L2 in the plane that passes through P and I to Li. The %3D the points A cul,), Find also the equations of Line L3 that passes through P in this plane nd is perpendicular to Le

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

Q: nd the distance from the point to the plane.   (3,3,8)​, 7y+3

A: Given, the equation of plane is                                       7y+3z=0and  point (3, 3, 8)

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

A:

Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

A:

Q: Find the equetion of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Equation of linex=3+ , y=1+t , z=2tIn carterian formx-03=y-11=z-02Line passing through 0,1,0 and…

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

A: Given:

Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

A:

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

A:

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

Q: Find an equation of the plane that is parallel to the plane x + 3y – 8z + 18 = 0 and contains the…

A:

Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

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

A:

Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

A:

Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

A:

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

A: According to the given information, it is required to find the positive value of c is the acute…

Q: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

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: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: Find the distance (d) from the paint (9, 4, 6) to the plane z-y = 5. STAAVE

A:

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

A:

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. a. Show that the planes are…

A: Given,

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Find equations for the planes The plane through (1, -1, 3) parallel to the plane 3x + y + z = 7

A:

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

A:

Q: Hiwed Find equations for_thefallawing lines - The line through (3, Sz=2) Perfendiculor toX-z plane

A:

Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (а) х…

A:

Q: a) Find the angle between the planes 2x+ 5y -6z 0 and 3x+ 6y + 8z= 0 b) Find the distance between…

A: Given: a) Planes 2x+5y-6z=0 and 3x+6y+8z=0. b) Planes 4x-y+2z-6=0 and 8x-2y+4z+6=0. To find: a)…

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: The planes 3x + 6z line. = 1 and 2x + 2y - z = 3 intersect in a a) Show that the planes are…

A:

Q: Find the angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

A:

Q: Find the point of intersection of the line L given by {(x, y, z) = (5,-1,1) +r(-3,-1,-5) rER} with…

A:

Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

A:

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

A:

Q: Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(−1, −2, −3) &…

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

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y + z =…

A:

Q: et L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane z +…

A:

Q: The plane can perpendicular to the a) x-axis at (3, 0, 0) b) z-axis at (0, 0, -2) c) y-axis at (0,…

A:

Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

Q: Find the intersection of the plane 3x – y + 2z – 3= 0 and the line

A:

Q: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

A:

Q: of the

A:

Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

A:

Q: Find the acute angle of intersection of the planes x + 2y – 2z = 5, 6x – 3y + 2z = 8 to the nearest…

A:

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Q: Find an equation of the plane through (-4, 3, –8) that is perpendicular to the line x – 2 = t, y +3…

A: Given line : x-2=t , y+3=2t ,  z=-tx-21=t , y+32=t , z-1=tx-21= y+32= z-0-1 comparing with standard…

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.