Let a be the plane containing the line Sy-z-2=0 | 2x + z = 0 and the point (0, 1,0). Which of the following statements is true? O (a) In the cartesian equation of a, the constant term is equal to zero. O (b) in the cartesian equation of a, both the z-coefficient and the y-coefficient are equal to zero. O (c) In the cartesian equation of a, the x-coefficient is equal to zero. O (d) In the cartesian equation of a, the z-coefficient is equal to zero. 040 s282412 1040 282412 01040 s282412 p1040 s282412 040 s28

Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

A:

Q: 2. Give the symmetric equations of the line l perpendicular to the plane T : 5x– 2y = z+4 and…

A: we have to find equation of line.

Q: The equation of the plane that contains the three points (1, 2, 0), (1, 3, 1), and (3, 0, 4) is 6x…

A: Cartesian equation of a plane passing through three non collinear points A(x1,y1,z1), B(x2,y2,z2),…

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

A:

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Let L be a line which passes through the point (-4,0, 1) and is perpendicular to the plane x + 2y +…

A: Please refer the attached image for complete solution.

Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: 4. Find the general equation of the plane passes through the points (3,2,1) and (3,1,–5), and is…

A: We have to find the plane equation

Q: An equation of a plane P passes through the point (0,0,-3) and perpendicular to the line L:x = 1-2t,…

A:

Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

A:

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

A:

Q: Find an equation for the plane passing through the point P(-2, 1, 1) and parallel to the plane 3x +…

A: Solve for the equation

Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

Q: (24 17. 3417.4) %3D Find the equation of the plane that contains the line x = 3t, y = 6 - t, z = 4…

A:

Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane r + 2y +…

A:

Q: Let L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane r + 2y +…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

A:

Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane r + 2y +…

A:

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

A:

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

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: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

A:

Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

A:

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

A:

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: 4 Let L be perpendiculor to the plane x+2y+ 62 -0 a line which passes thraugh the polnt (-6,0,1) and…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

A:

Q: Find an equation of the plane with the given characteristics. -4 The plane passes through the point…

A:

Q: The z-coordinate of the point of intersection of the plane r+2y +z= 6 and the line through the…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane r+ 2y +…

A:

Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane x + 2y…

A: Direction ratio of Line is < 1,2,6> Write equation of straight line and solve it with plane to…

Q: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane r + 2y+…

A:

Q: Let P be the plane with equation x-2y+2z =-10. Find four distinct points on P at distance 6 v2 to…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

A:

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A:

Q: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by,…

Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

A:

Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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.