Consider the plane makes intercepts of 2 A, 3A, 4A on the coordinate axis of the crystal with a:b:c=4:3:2. The crystal is orthorhombic crystal. Calculate the miller indices of the given plane of the crystal. (A) (4,1,1) (B) (4,3,2) (C) (4,2,1) (D) (4,4, 4)

Q: Find the equation of the plane with the given description. Passes through (6, 1, 5) and is parallel…

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Q: Find the distance from the point to the given plane. (1, -4, 6), 3x + 2y + 6z = 5

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

Q: Find an equation for the plane consisting of all points that are equidistant from the points  (−5,…

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Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: The equation of the plane passing through the point (0, 0, 4) and perpendicular to 4 is: the line 4…

A: Equation of plane

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: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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

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Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

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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: Consider the points P = (2,-1,4), Q=(1,1,1), and R=(3,1,-2) in xyz-space. An equation of the plane…

A: Solution is given bellow

Q: Consider the plane with equation 3x – 2y + 4z =7. A point has x coordinate 1 and y coordinate 2. If…

A: We have to find z coordinate

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

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Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c  And, the plane is, Ax+By+cZ+D=0

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Determine the general equation of the plane N passing through the point P(3, –1,2) and parallel to…

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Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Find the equation of the plane having the points P(1, 2,5), Q(-2, 0, 1), and R(-3,-4,1). 8x + 2y 5z…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Find the point p(x, y, z) on the plane 2x + y - z - 5 = 0 that is closest to the origin.

A: Given:The given plane is 2x+y-z-5=0 that is closest to the origin.To find:we have to find…

Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: 6) Consider the plane P : x+y – z = 0 in K³ that contains both the points P1(1,0, 1) and P2(-1,1,0).…

A: Given : plane P : x + y - z = 0  & Points P1(1,0,1) & P2(-1,1,0) To find :  1. Equation of…

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

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Q: Find the point where the point P(1,3,4) is symmetrical with respect to the plane D:3x-2y+z+6=0

A: In this question we will use basic of geometry i.e image of a point in a plane. Solution of the…

Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

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 the distance from the point (-2, 1, 4) to the plane z = -1

A: Given, plane z=-1 and the point (-2,1,4)we have to find the distance from the given point to the…

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

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Q: Consider the plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , .  Here, the points are .

Q: Find the equations of planes passing through point (a,0,0) if these planes intersect one-sheet…

A: As per the question we have to find the plane which is tangential to the surface of the hyperboloid…

Q: Find the point on the plane 2x + 2y + 5z = 2 that is closest to the point P(- 3, 5, – 5). (x, y, z)…

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Q: 2. The plane with equation: 7 = (1,2,3) + m(1,2,5) + n(1,–1,3) intersects the y- and z- axes at two…

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Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: The general equation of the plane that containsteh points (1,0,3),(-1,1,-3)and the origin is of the…

A: Given general equation of plane is

Q: Find the point on the plane 5x +4y+z 12 that is nearest to (2,0,1). What are the values of x, y, and…

A: The plane 5x+4y+z=12Normal vecor of the plane               <5, 4, 1>The point we seek would…

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.