Question 5 Let A = (2, 1,0), B = (1,2, 0) and C = (1,1, 2) be points in R³. (i) Find the equation of the plane passing through A, B and C. (ii) Hence, find the shortest distance from this plane to the origin O. You are given that the volume of a tetrahedron is given by the formula V = }bh, where b is the area of the base and h is the perpendicular height. Use your answers to parts (i) and (ii) to find the volume of the tetrahedron with vertices at 0, A, B and C. (iii)

Q: Question: find the hyperbolic distance between (0,10) and (3,4)

A: Formula Used: Hyperbolic distance between two points (x1,y1) and (x2,y2) is  distHx1,y1 , x2,y2 =…

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A:

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A: The Distance between a point to the plane  is given as follows

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A: Given, the two spheres in 3-space. The first sphere has radius 5 and is centered at the origin (0,…

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A: Solution

Q: 3. Let OÁ = i +2j+ k, OB = 3i+j+2k and OC = 5i+j+ 3k. (a) i. Find AB × AČ. ii. Find the area of…

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Q: Suppose a plane through three points A(1,-2,4), B(1,-1,6) and  C(2,0,5). Solve the following two…

A:

Q: A sphere, Si is given by the equation: r? + y² + 22 – 2x – 4y + 8z + 17 = 0 (a) Write the equation…

A: (a) Consider the given information. x2+y2+z2-2x-4y+8z+17=0 Now, write the equation in the standard…

Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

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Q: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Find the equation (formula) of a sphere with radius r and center C(h, k, 1) and show that x² + y²…

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Q: Question4 : We have two planes in R', defined by equations x – 3y + z = -7 and 2x + y + 2z = 0.…

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Q: 16. Consider the equation of the surface S given by z = 3r*ya + 3y – 4 Where a is an even number and…

A: Linear approximate equation is the equation of tangent plane.

Q: The distance from the point S(7, 7, -6) to the plane 2x + 11y + 10z = 9

A: option C 2215 is correct detailed solution is given below

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Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

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