For what positive value of c is the acute angle between the plane containing the points A(0,0,1), B(0,4,0), C(c,0,0) and the yz-plane equal to 60 degrees?

Q: If the plane ax+14y+cz=30 through the point P(2,3,−1) is orthogonal or perpendicular to the plane…

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

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Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: The equation of the plane passing through the three non-colinear points x1,y1,z1, x2,y2,z2, and…

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Find a plane through the origin that is perpendicular to the plane M: 2x + 3y + z = 12 in a right…

A: Given equation of plane is

Q: Find the distance (d) from the point (– 6, – 8, – 7) to the plane 5x – 2y + 2z = 25. - d =

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Find the acute angle (in degrees) between the planes 5x 4y – 2z = 8 and 5x 2y – 5z = 5. %3D %3D

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Q: Find the angles between the planes 5x + y - z = 10, x - 2y + 3z = -1

A: Solution -  We have equation of two planes -  Plane 1 -…

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

A: Symmetrical point at plane problem....

Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

Q: Determine the angle between the planes: x-z+7=0 2x +y-z+8 = 0

A: Solution :--

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: Find the angle (in degrees) between the planes 4y + z = 4 and – 4x + 2z= - 3.

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Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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Q: 25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E…

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Q: Find the angle between the planes 3x-6y – 2z = 15 and 2x +y – 2z = 5

A: Recall: Vector method, cos θ=n1·n2n1n2 We have, n1=3i-6j-2k, n2=2i+j-2k

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

A: Given : 2x+2y+2z=3 and 2x-2y-z=5   To find: Angle between planes   we know that for plane Ax+By+Cz=d…

Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x – 2 y-z 5

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Q: Find the distance (d) from the paint (9, 4, 6) to the plane z-y = 5. STAAVE

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Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z =v 6, then 2cos (0) = 0 1 O 2 1/2…

A: Angle between planes is defined as angle between their normals.    Option  C is correct answer

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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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: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y- z = 5

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Q: x − 3y + 6z = 4 e 5x + y − z = 4

A: For the equation of plane a1x+b1y+c1z+d1=0, a2x+b2y+c2z+d2=0The angle between them is given…

Q: Is it possible to find a plane perpendicular to both i and j? Explain why.

A: The objective is to find a plane perpendicular to both i and j, if possible.

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: Find the angle between the planes x+ y=1 and 2x+у-2z32?

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Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

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: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: Find the cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

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Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

Q: Determine whether the planes 2x − z = 1, 4x + y + 8z = 10 are parallel, orthogonal, or neither. If…

A: 2x-z=1,  4x+y+8z=10 Now comparing with a1x+b1y+c1z=d1  &  a2x+b2y+c2z=d2, we get a1=2, b1=0,…

Q: 8. What is the angle between the two planes x+y=0 and y-z=2?

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Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

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Q: The acute angle of intersection of yz plane and the plane 2x-y+z-4=0 is:

A: Let A1x+B1y+C1z+D1=0 and A2x+B2y+C2z+D2=0 be the equation of two planes aligned to each other at an…

Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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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.