1) Find the equations of the line that passes through point Q(1, 2, 1) and is perpendicular to the plane x-y + 2z - 1 = 0.

Q: Find an equation of the plane. The plane that passes through the point (−2, 1, 3) and contains the…

A: Given that, Two planes are following, x + y - z = 2 3x - y + 4z = 3 And the point is following, (-…

Q: Find an equation of the plane containing the point P (1, -7,1) and the line r (t ) = .

A: Given: The point P (1, -7,1) and the line r (t ) = <3 − 2t, 4t, 7> . So,             x = 3 −…

Q: Write the equation of a plane that intersects at the coordinate axes OX and OY segments 2 and -17…

A: Given that: Intercepts of  a plane with coordinate axes: OX=2 and OY=-17and Plane passes through…

Q: 18-20 Find an equation of the plane. 18. The plane through (2, 1, 0) and parallel to x + 4y - 3z = 1

A:

Q: (a) Find the point at which the given lines intersect. r= (1,3, 0) + t(3, -3, 3) r = (4, 0, 3) +…

A:

Q: 2. Find a plane perpendicular to the planes x + y - 3z = 0 and x - 2y-2z = -1. Your answer

A:

Q: Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find…

A:

Q: The plane with equation 11x+2y-3z-6=0 intersects the y- and z- axes at the points A and B…

A: The point at which the plane intercept an axis will have other 2 axes as 0. Therefore, the…

Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

A: For the solution follow the next steps.

Q: (A) Find the angles between the planes 2 x + 2 y+ 2z = 3 and 2x- 2 y-z = 5 (8) Find the distance…

A:

Q: Two planes x+ y – 27 = 3 and 2x – 3y + z = 1 intersect in a line. a Find the Cartesian equation of…

A: (a) Given that planes are x+y-2z=3 and 2x-3y+z=1 The cartesian equation of the two lines is,…

Q: CAn equation of the plane through the point (2, 5, 7) that is parallel to the line 7 (t) = 3î + 2ĵ -…

A: Given problem:-  Find an equation of the plane through the point (2, 5, 7) that is parallel to the…

Q: (a) Find the point at which the given lines intersect. (1, 2, 0) + t(2, -2, 2) = (3, 0, 2) + s(-2,…

A:

Q: 24. Let A = (2,1) and B = (-1, –2) be two points on the plane. Write the equation of the line which…

A:

Q: Find an equation of the plane. The plane that passes through the point  (−2, 1, 3)  and contains…

A: Question : Find an equation of the plane.   The plane that passes through the point  (−2, 1, 3)  and…

Q: Find the linear equation of the plane through the point (2,6,9) and parallel to the plane…

A: Equation of plane parallel to  x+5y+4z+4=0 is given by,x+5y+4z+4+λ=0

Q: Linear Algebra Let "r" be the line determined by the intersection of the planes x+yz= 0 and…

A:

Q: QI/ Determine whether the two planes are parallel or intersecting. Find their line of intersection…

A:

Q: (a) Find the point at which the given lines intersect. r = (3, 2, 0) + t(2, –2, 2) r = (5, 0, 2) +…

A: Consider the equations of lines

Q: (a) Find the intersection point of the lines ri(t) = (3, 2, 0) + t(2, –2, 2) and r2(t) = (5,0, 2) +…

A: Solved below

Q: Find parametric and symmetric equations of the line (i) through the points A(1, −2, 3) and B(2, 0,…

A:

Q: 5) The equation for the plane through A(2, 0,0), B(0,1,0), C(0,0,5) is

A:

Q: The plane The plane that passes (0, 1, 5), (2. -1, 6), and (3, 2, 5). through points

A: Given:  Points: ( 0 , 1 , 5 ) , ( 2 , -1 , 6 ) , ( 3 , 2 , 5 )

Q: (a) Find the equations of the line through the points (4, −1, 2) and (3, 1, 4).(b) Find the equation…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: Show that planes 2x- y + z = 0 and x+2y-z = 1 intersect according to a straight r.

A: General Equation of a Plane: A plane can be represented by an equation of first degree in such as…

Q: Relay Question: (i) Find the distance from the point P(-1,2,1) to the plane II1 : 2x + y – 3z = 4.…

A:

Q: 3. - The points A(1,0, 0), B(0, 1,0) and C(0,0, 1) all lie on a same plane. An equation of the plane…

A: If points A,B and are on the same plane , they will satisfy the equation of plane.   Point C (0,0,1)…

Q: Linear Algebra  Determine the line r that passes through points A(4, 0, 1) and B(5, 1, 3). Then…

A: we have to determine the equation of a line r passing through points A(4,0,1) and B(5,1,3). then we…

Q: -> Moving to another question will save this response. uestion 11 Write the equation for the plane.…

A: Note:-  According to Bartley guidelines we can do only one question so please upload the next…

Q: Let A(2, 1, 1), B(1, 2, 1), and C(1, 1, 2) be three given points. Find (i) parametric and symmetric…

A: Let A2,1,1, B1,2,1, and C1,1,2 be three given points. Find (i) parametric and symmetric equations of…

Q: Question Find the equation of the Plane through the point (-1,4,2) that contains the line of…

A: Given: The equation of line of intersection of the planes are, 4x-y+z-2=02x+y-2z-3=0 The objective…

Q: Equation for the plane through A(2, 3, 1), B(1, 5, 7) and C(-1,1, 1) is- Select one: А. 6х — 9у — 42…

A:

Q: Consider the lines below. r = ‹2, 2, 0› + t ‹2, -2, 3› r = ‹4, 0, 3› + s‹-2, 2, 0› (a) Find the…

A:

Q: 18. Find the equation of a plane that passes through the points A(3,-1,2), B(6, 4, 1) and C(2,0,-3).…

A:

Q: Q/ Find the angle between the planes (x+y+2=1)and (x-24+32%-1).And find the Symmetric equations for…

A:

Q: a) Find an equation of the line in space through the points S(-1,-4,8) and T(2,-1,2). b) Find the…

A:

Q: Linear Algebra Let α be the plane that passes through the origin and is perpendicular to the line…

A:

Q: (a) Find the point at which the given lines intersect. r = (1, 2, 0) + (2, -2, 2) r = (3, 0, 2) +…

A: The vector form of the equation of a line is r=ro→+tv→. The equation of the plane containing the…

Q: a. Find an equation of the plane that passes through (3, 2, -1) and contains the line l(t)= (-t, 2,…

A:

Q: 22. a) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…

A:

Q: 2- Find un equation 6f the Plane containing the Points (0,0, 2 ), o (2,q!) (-2,3,3).

A:

Q: (a) Find the equation of the plane that contains the point (-1,5,0) and is orthogonal to the plane…

A: Use the following formulae, to obtain the solution. The equation of the plane containing the points…

Q: 18. Find the equation of a plane that passes through the points A(3,-1,2), B(6,4, 1) and C(2,0,-3).…

A:

Q: Question Find the equation of the Plane through the point (-1,4,2) that contains the line of…

A: Applying family of planes to solve the problem

Q: caining points (0, 1, 2), (3, 3, 4), and (4, – the point (-1,5, 0) and the plane cont t (a).

A:

Q: Find an equation of the plane. The plane through the points  (0, 9, 9), (9, 0, 9), and (9, 9, 0)

A: A per our guidelines we are instructed to answer one question at a time. Submit the second question…

Q: a) Find the equation of the plane that goes through three points A(0,3,4), B(1,2,0) and C(-1,6,4).…

A:

Q: Ноше work Find an equation of plane through the points pl (-1, 1, 1) and point intersection of the…

A: Here we have to find the equation of the plane passing through the point P1(-1,1,1) and point of…

Q: Write the equation for the plane. The plane through the point P(-4, -4, 3) and parallel to the…

A: Explanation of the answer is as follows

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.