Let r = ri+y1j+z¡k, r2 = 1zi+ Y2j + zzk and r3 = r3i+ yaj + z3k be the position vectors of points P(r1, y1, 21), P2(r2, 42; 22) and Ps(r3, Y3, 23). Find an equa- P. tion for the plane passing through P, P2 and Ps. See fig- ure on the right

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A: Given,     (a) (0, 0, 1); (1, 0, 0); and (1/2, 1/2, 0)  (b) (1/2, 0, 1); (1/2,0, 0); and (0, 1, 0)…

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Q: Let r¡ = r¡i+yj+z¡k, r2 = rzi+ Yzj+ zzk and r3 = rzi+ Yzj+ z3k be the position vectors of points…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

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Q: is ndicular tò the plane containing the points: A = (-1,1, 2) B = (-3, 2, 1) C = (5 – 1, 1) the

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 %3! +3y +z 8 Find the normal vector, n,,…

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Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

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Q: Let ri = xi+yıj+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

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Q: Show that the vector V = (x+ 3y)i + (y – 32) j+(x – 2z)k is solenoidal. %3D

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Q: a) Find the distance between two skew lines L1 and L2 such that L1: 1+ 4t, y=5-4t, z=-1+5t  L2:…

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

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A: given vectors A→=2x^1-6x^2+2x^3 and B→=4x^1+3x^2-x^3 find the unit normal vector plane spanned by…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 2t x + 3y + z = 7 Find the normal…

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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.