Given the two planes: II : x + 2y +3z= –1, II2 : 2x + 5y +14z = 11, tis true that: a) The line L formed by intersecting both planes has equation: x = -27+ 13t %3D L:{y= 13 – 8t z=t, teR. b) c) The intersection of these planes is either of them. since they are the same plane d) There is no intersection line between these two planes, because they are parale e) The line L that is formed by intersecting both planes has equation: x = 13 – 105t L: y=-8+13t

Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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Q: 1. State the definition of a rhombus and one property which applies only to a rhombus but not to any…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: The diagonals of an isosceles trapezoid ABΓΔ (ΑΒ // ΓΔ) intersect at O. If E, Z, H, Θ are the means…

A: Given an isosceles trapezoid ABΓ∆ . Its diagonals intersect at O. Given that the mid - points of OA…

Q: Match the theorem or rule for what it justifies IF the quadrilateral is already proven to be a…

A: Given:

Q: The distance from a point S(xo,yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n · PS| d In|…

A: From a point S(x0,y0,z0) to the plane M = ax+by+cz+d=0 Let S1=x1,y1z1 be any point in the given…

Q: The definition of a rhombus is a quadrilateral that has four congruent sides. O True O False

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Q: A plane P cuts sphere O in a circle that has diameter 20. If the diameterof the sphere is 30, how…

A: We have given that we have a plane P that cuts the sphere with center O having diameter 30 units  at…

Q: Considering only the 4-point planes that are drawn in the figure below, which point does NOT share a…

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Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

Q: Show that quadrilateral RSTV is an isosceles trapezoid. y v (a + d, e) T (c - d, e) R (a, b) S (c,…

A: We have to show that quadrilateral RSTV is an isosceles trapezoid. A trapezoid is a quadrilateral…

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

A: Introduction :

Q: Which is the fourth point on plane TSW? T. U O Y

A: A plane is a 2-dimensional surface. It can have an infinite number of points. A plane is composed of…

Q: Given: OPQRS with diagonals PR and SQ intersecting at T. (Refer to figure below for nos. 1-6) A. If…

A: A. PQRS is a rectangle and diagonal with PR and SQ intersect at T. We know that all the angles of a…

Q: Prove that the sum ofthe squares of the sides of a rhombus s equal to the sum of the squares of its…

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Q: Are these planes parallel?

A: The given planes are 2x+y-z=2 ............. (1)                                   2x+3y+5z=4…

Q: iven two line segments, construct a rhombus whose diagonals have lengths equal to the lengths of the…

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Q: 1. Consider the planes P and Q given as 2x- 3y +2 = 3 and 4x- 6y + 22 = 5. Are P and Q parallel?…

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Q: 3x + 30 (5y 2)° 5z +5 8х — 5 (9y 8) SR = RT mZT AS 4z 8 %S4

A: we will find in next step

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: nat is

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Q: 4. Determine whether the planes are between them. 2x – 3y + 4z = 5; x+ 6y + 4z = 3 parallel,…

A: This question can be solved using the concept of angle between two planes.

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

A: Recall: Mid point Formula: The midpoint of M(x,y) of the line segment from A(x1,y1) to B(x2,y2) is…

Q: Determine if the three planes -x-5y-5z= 2, 4x -5y +4z = 19 and x +5y - z = - 20 have an intersection…

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Q: Consider the two planes in R3 given by the equations: x+2y+3z-10=0, and-2x-4y-6z+1=0

A: The planes ax+by+cz+d=0 and ex+fy+gz+h=0 are parallel when the relation ae=bf=cg is satisfied. The…

Q: 5. What can you change to the two planes to make them parallel? Make as few changes as possible and…

A: given planes π5: 2x-4y+2z-2=0π6: x-y+3z-2=0

Q: Describe the intersection of the horizontal plane z = h and thehyperboloid −x 2− 4y 2 + 4z 2 = 1.…

A: Put z=h in given equation -x2-4y2+4h2=1⇒x2+4y2-4h2=-1

Q: Show that the planes given by 2x − 4y − 3z = 5 and −4x + 8y + 6z = 1 are parallel, and find the…

A: Solution:Given2x − 4y − 3z = 5 −4x + 8y + 6z = 1To prove :The planes are parellel and to find the…

Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +…

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1…

Q: If the four straight lines ax + by + p = 0, ax + by + q = 0, cx + dy + r = 0 |(p-4)(r-s) bс - ad and…

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Q: Prove that the distance between parallel planes with equations

A: Given : Two planes with equations n·x=d1 and n·x=d2

Q: Do the three planes, x+y−3z = 2, 2x+y+z = 1, and 3x+2y−2z = 0 have a common point of intersection?…

A: Fact 1 :Three planes a1x+b1y+c1z=d1                    a2x+a2y+c2z=d2…

Q: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: Given: OPQRS with diagonals PR and SQ intersecting at T. (Refer to figure below for nos. 1-6) A. If…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. The diagonals of rhombus RSTV intersect at U. Given that mZURS =71° and RV = 44, find the…

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Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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Q: Prove that the diagonals of a rhombus intersect at right angles. (A rhombus is a quadrilateral with…

A: We have to prove that diagonal of rhombus intersects at right angle. Let ABCD is a rhombus.…

Q: Given the planes (x, y, z) = (0,0, –3) + s(1,1,–2) + t(-2, –-1,3), and x + y + z + 6 = 0 : a) Are…

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (а) х…

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Q: ABCD is a rhombus with sides AB and BC. If AB : %3D 12x - 2 and BC = 3x + 7. Find CD. CD =

A: In rhombus ABCD, AB = 12x-2 BC = 3x+7 To evaluate : The side length CD

Q: Are the planes given by Π1 : 2x − 3y + z − 1 = 0 and Π2 : 3x − 2y + 4z − 7 = 0 parallel? Justify…

A: Here, the normal vector of the plane1 is: n1=(2,-3,1)  and the normal vector of the plane2 is:…

Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: The midpoint of AB is M(6, 1). If the coordinates of AA are (4, 8), what are the coordinates of BB?

A: M has coordinates (6,1) Coordinates of A =(4,8)

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n PS| d =…

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Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: The midpoint of AB is M(1,3). If the coordinates of A are (-1, 5), what are the coordinates of B?

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Q: P, Q and How far is the point S from the plane that contains the points R?

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: On the sides of a triangle ABC, squares ABDE, ACFG, BCJK are constructed externally to it. BF, AJ,…

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Q: The midpoint of AB is M(1, 3). If the coordinates of A are (-1, 5), what are the coordinates of B?

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