3. Let A, B and C be the points with position vectors 2 a = -- (:)). - (1) · - - () 1 b= 5 C = 3 respectively, and let II be the plane which contains the points A, B and C. (i) Find a Cartesian equation for the plane II. (ii) Find the distance between the plane II and the point with coordinates (0, 1, 0) (i.e. the point whose position vector is j). (iii) What is the position vector of the point on II which is closest to Q?

Q: 8. Find the parametric equations for the plane that passes through the points: P (2, -2, 3), Q (0,…

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Q: 5. Let II be the plane with equation x+y+z= 3, and let II₂ be the plane with equation 3x + 4y + z =…

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Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

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: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…