5. Find the parametric and symmetric equations of the line through the two points P = (-2, 2, -1) and Q = (1, -5, 3). a= (x2-Ki, Yz-9,22-2,) ズ- (1-レ-2),1-5-2), (5-1-1) (3,-7, +> Symmetric: X+2: Z+1 y-2 = 4 %3D 3 -7 ニ a b c Parame tric :(= -1+ 3t リ= 2-7t %3D %3D

Q: Find the equation of the plane passing through the points (1,0, -1), (-1,2,1) and parallel to the…

A:

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A:

Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Find parametric equations for the line that passes through the points P(-3,7,9) and Q(4, 1, -5).

A: The given points are P-3,7,9 and Q4,1,-5. The line containing the point x0,y0,z0 and parallel to the…

Q: 8. Determine the Cartesian equation of the plane that contains the line 7=(2, 3. 2) + 1, 1.4), te R.…

A: According to guidelines we solve one question.thanku

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

A:

Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

A:

Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

A:

Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

A:

Q: Determine the symmetric equations of line that passes through the points B and С.

A:

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

A:

Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x - 5y…

A:

Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

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

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

A:

Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

Q: 3- Find an equation of the Plane perpendicular to the line through (2,2,-9) and (7,-1,3) and…

A: To Find: Equation of plane perpendicular to the line through the points (2,2,-9) and (7,-1,3) and…

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: Find parametric equations for the line through the points P(-1,-1, 7) and Q(3, -4, -1) O x = 4t - 1,…

A:

Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

A:

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

A:

Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: Find the equation of the plane containing the point (4, -1, 3) that is parallel to the plane 2x - 3y…

A:

Q: The plane with equation = (6,-2,3)+a(1,3,0) + b(2,2,-1) intersects the y- and z- axes at the points…

A: Vector equation of line is r'→=a→+αb→-a→where, a→ is the position vector of the point A.…

Q: as If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to…

A:

Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A:

Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

A:

Q: Find the equation of a plane passing through points (3,2,2), (1,0,-1) and parallel to the line…

A: Equation of plane is calculated as below:

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

A:

Q: Find the parametric and symmetric equations for a line that passed through the points (2,0,8) and…

A: Representing the points as the points vectors we get,  2,0,8 and -2,6,4 The direction numbers are…

Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

A:

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

A:

Q: Find an equation of a line containing the point (1, 7, -3) and parallel to the yz- plane.

A:

Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

A:

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

A:

Q: find the equation of the plane passing through (1,0,-1)&(-1,2,1) and parallel to the line of…

A:

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A:

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

Q: Find parametric equations for the line segment joining the points (-6, 7) and (4, 5). x=7-2t, y…

A:

Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

A:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

A: