Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar + by + cz + d = 0 is Jaxo + byo + czo + d| Va? + P + c²

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

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: 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: Use Green's Theorem to calculate ( - sen(a))da + (2a + 3)dy, where C is the triangle with vertices…

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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: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

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: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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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: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Find the angles between the planes in Exercises 47 and 48. 47. x + y = 1, 2x + y - 2z = 2 48. 5x + y…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: Indicate on an xy-plane those points (x, y) for which the statement holds. |x − 3| ≤ 5 and |y + 2|…

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Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: 4. Calculate the perpendicular distance between the plane with axis intercepts P(4, 0, 0), Q(0, 3,…

A: Answer is: 0.53846153846153846 Solution is given below:

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: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

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: ind the equ.of Plane that Contains plos1,3) and Parallel to the X-2 Plane and PerPendicular to the…

A: Solution:-

Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)

A: We need to show that the projective plane of order n indeed gives a BIBD (n2+n+1,n+1,1)

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

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: Is the line x = 4+ 2t , y =-t , z = -4t – 1 parallel to the plane 3x + 2y + z = 7? %3D

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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: Prove that the distance d from a point P (xo, Yo, 2o) to the plane r: Ar + By + Cz + D = 0 is given…

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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: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

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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: 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: A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor…

A: let the normal vectors for the vectors be a1, a2 thus a1=<1,1,-1> and a2=<2,-3,4>. Let…

Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z+ 6 = 0 is 3.7 True O False

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Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

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Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

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 shape ABCD is a rhombus. With A(1, 4), B(3, 0), C(1. -4) and D(-1,0).

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Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: et L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane z +…

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Q: The plane can perpendicular to the a) x-axis at (3, 0, 0) b) z-axis at (0, 0, -2) c) y-axis at (0,…

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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: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

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

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Q: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

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