5. The line passes through the point (-4, 5, 2) and is parallel to the xy-plane and the yz-plane. 6. The line passes through the point (2, 3, 4) and is perpendicular to the plane 3x+2y-:=6.

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: The plane passes through the point (18, -16, 9) and contains the line given by = = z . 1.

A:

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

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

A:

Q: 2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: 2. Find the exact value of the distance between the line of intersection of the planes 2x - y + 2z =…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

A:

Q: 5z' + 3z gral z² - 4 plane, is

A:

Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Find a line passing through (−2, 5, −3) and perpendicular to the plane 2x − 3y + 4z + 7 = 0.

A: we have to find a line passing through (-2,5,-3) and perpendicular to the plane 2x-3y+4z+7=0   as we…

Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

A: We know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

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 distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

A:

Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

A:

Q: The distance between the point (9, 8, 3) and the plane x + y−2z = 5 is _____.

A:

Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

A:

Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x = −6+t,…

A:

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A:

Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

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

A:

Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

A:

Q: Find the distance from the point (1, -4, 4) to the plane −2x−4y+3z=5

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A:

Q: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

A:

Q: The distance from (6,-7, 10) to yZ-plane is

A: Concepts let (x, y, z) be a point then  1) distance of the point from XY plane is…

Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

Q: 4. Find the equation and sketch the graph of a plane that is parallel to the yz-coordinate plane and…

A: We know that equation of plane parallel to yz-coordinate plane is given by: x=k where k is some…

Q: Find the distance from the point (5, -4, 1) to the plane −3x−2y−3z=−4

A:

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

A:

Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

A:

Q: The line passes through the point(7, 8, 9) and is parallel to the xz-plane and the yz-plane. 7,8,1 +…

A:

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

A:

Q: Find the distance of the point (3,8,2) from the line x-1 -y+3 -z+2 measured -3 2 -4 parallel to the…

A: Given point 3, 8, 2Given line - x-12=-y+3-4=-z+2-3Let the parameters be equal to an arbitrary…

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

A:

Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

A:

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

A:

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find the equation of line and then find its intersection with the plane

Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.