2. The equation of a particular paraboloid is z = x² + y². Determine the point(s) of intersection (if [0, 4, 6]+[3, 1, -17] any) of the paraboloid and the line [x, y, z]=

Q: 6. [8.5] Consider the points A(1, 3, 1), B (2, 1, 0), and C(5, 1, 1). Determine the Cartesian…

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Q: 4. Consider the points A(1, 0, 3), B(-1, 5, 2) and C(3, -1, 1). Find the equation of the plane…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 1,1), and R(1,1,0). Write the…

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Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z][-1, -9,16]++[3, 3,…

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Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

A: Given points P1,3,2, Q3,-1,6, R5,2,0

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Which of the following  points in the standard (x, y) coordinate plane is furthest from the origin

Q: 1. Let points A, B, C, and D be as follows: A=(3, 1, 2), B=(-1,3,5), C= (0, 2, 2), D =(4, 5, 1) a)…

A: The distance of a plane is defined as the algebraic expression that gives the pairs of points in the…