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: Find an equation of the plane that passes through the points A(2, 1, 1), B(-1, -1, 10), and C(1, 3,…

A: our objective is to find the equation of plane.

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

A:

Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

A:

Q: Let I be the line with parametric equations x = -9-2t y=-10+3t z=4+t Find the vector equation for a…

A:

Q: Let A= (-1,3,3) B= (4,-1,0) C= (5,4,-7) D= (2,-1,-1) i) the normal vector to the plane ABC. ii) the…

A:

Q: 3. (a) ) The points A(5, -10) and B(-7,6) are the ends of a diameter of circle C, Determine the…

A:

Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

A:

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

A:

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

A:

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: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

A:

Q: 9. (a) What are the two properties that determine a line in space? Give parametric equations for a…

A: To find the parametric equations for the line through the given points and to mention the properties…

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

A:

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

A:

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

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…

Q: 180 70° 40 D X85° s92 9216

A: Length of arc = θ3602πr Where θ is angle suspended from centre and r is radius of circle .