Problem 1: Let P, be the plane defined by the equation 2x – 8y + 5z = 2 and let P2 be the plane defined by the equation 3x + 2y – z = 7. Find the equation for the plane which is perpendicular to both P1 and P2 and which passes through the point (-3,1,2). Hint: If P3 is perpendicular to P, and P2, then the normal vector of P3 will also have to be perpendicular to the normal vectors of both P, and P2. Feel free to use Mathematica

Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

Q: If a line is parallel to the vector 8i + 5j + 3k and passes through the point P = (6,2,4), then the…

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Q: (a) For what value of kwill the lines X₁ k 2 -0------ +t₁-2 and X₂ = -3 = + t₂ intersect?

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Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

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Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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Q: 1 I 4 x 4 x 4 49. lim-

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Q: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

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Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

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Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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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.