Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z –8 = 0, and (üi) 2x + 35y - 39z + 92 = 0, have a common line of intersection. Prove that the point in %3D which the line 3 e-1 y z- 3 meets the third plane is %3D 1 | equidistant from other two planes.

Q: Find an equation (in standard form and in general form) of the plane containing the points (2, 1,…

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Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

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Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Find the equation of the plane that passes through the point (10, -8, 5) and contains the line y-2…

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Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

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Q: Determine the point on the graph of z = x² + y²+ 10 closer to the plane x + 2y-z = 0

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Q: Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes…

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: A point P(x, y) moves so that the sum of the squares of its distances from points A(0,0)and B(2,-4)…

A: Given,           A point P(x, y) moves so that the sum of the squares of its distances from points…

Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1, –1,9), (4,…

A: First we have to find Normal vector of both planes.

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

A: Vertices of triangle ABC are A(2,-3) , B(-2,1) and the centroid of this triangle moves on the line ,…