QUESTION 2 What is the best descriptor of the object in three-dimensional space given by the equation x +2y=6? O a. A line on the xy-plane. O b.A line that is not contained in the Xy-plane. OC.A plane containing the z-axis. O d.A plane parallel to the Z-axis. O e. A plane that is not parallel to the Z-axis.

Q: Consider the points A=(2,7,-4) and B=(4,5,7) in R3, one way to write the parametric equation of the…

A: Given :- Consider the points A = (2, 7, - 4) and B = (4, 5, 7) in R³, To find:- one way to write the…

Q: Question 7 The equation of the sphere with center (5, 6, 5) and satisfied by the point (6, 3, - 1)…

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Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: The equation (x − 1)² + (y − 4)² + (z − 3)² = 25, - is an equation of the sphere with center C(1,4,…

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Q: QUESTION 2 Which of the following describes a different plane than the other three? O a. x +2y+3z 6…

A: The  direction cosines of a) is 1,3,2  For the remaining options direction cosines 1,2,3

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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Q: Question 4 In which of the following planes does the curve of intersection of the quadric surfaces…

A: find the equation of plane which lies in the intersection of the s

Q: Question 4: A plane parallel to y-axis passing through line of intersection of planes x + y + z = 1…

A: A plane parallel to y-axis passing through line of intersection of planes  x + y + z = 1 and 2x + 3y…

Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any non-zero numbers a, b, and c. Which planes…

A: The graph of given plane is,

Q: Question 8 (2 marks) The graph of (=) + (2) + (-) = 1 is a plane for any nonzero numbers a, b, and…

A: Solution

Q: By setting one variable constant, find a plane that intersects the graph of z=9x^2−3y^2+1 in a:…

A: Given that -  z=9x^2−3y^2+1

Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

A: Two planes are neither perpendicular nor parallel.

Q: Find the distance from the point (-1, -1, -2) to the plane - 3x – 2y + 1z = -4. Hint: See "Planes"…

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Q: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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Q: Problem 1. Let L be the line (2t, t, t — 1), t ≤ R, and A the point (1,1,-1). Let P be the plane…

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Q: Consider the following equation of a quadric surface. y? z? x? 144 144 = 1 144 a. Find the…

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Q: You are given the following points: A = (11, –14, –16), B = (16,0, 5), C = (-9, 16, 13). Which point…

A: Answer

Q: Question 7. The plane is perpendicular to the vector ỹ = i+j+k and contains the point Р- (3, —4,…

A: solution of the given problem is below...

Q: Question 2. Find the equation of the plane passing through the points (0, 1,0), (2, 1, 4), and…

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Q: You are given the following points: A = (11,20, –-18), B= (19,0,3), C =(-7,10,14). Which point is…

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Q: Question 2 Find the domain: X-y f (x.y) = x2+x-6 O {(x, y): x# -3 and x # 2} O (x, y): x - y 0} O…

A: The function should be well defined. For this function to be well defined, denominator must not be…

Q: Which of the following is the equation of a plane parallel to the yz-coordinate plane and passing…

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Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: Name two planes that intersect in FG.

A: We have to name the plane which intersects in FG,

Q: Problem 3. A plane, P, in R contains the point (-5; –-1; –3) and has normal (2; -4; 2)". Find the…

A: Given that: The point is: (-5, -1, -3)and the normal is: (2, -4, 2)T

Q: Problem 1. Let L be the line (2t, t, t — 1), t € R, and A the point (1, 1,-1). Let P be the plane…

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Q: Please consider α, β y t as real constants differents to 0. A possible graphic representation for…

A: Given  α, β y t as real constants

Q: Identify the surface in Cartesian coordinate for each of the following equations. a) p=5 and b)…

A: Given equations are in polar coordinates and we have to write their equation in Cartesian…

Q: Which of the following represents the equation of the surfaces with the following four views? Freet…

A: To find which of the following represents the equation of the surfaces with the given four views.

Q: 1.3 Show that the following equation represents a sphere, and find its center and radius. x2 + y2 +…

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Q: 2. Do the two planes intersect? If they do, where do they intersect? TT 2x - y + z = 1 = 0 3 TT 4 x…

A: Equation of the line perpendicular to the given plane be n1 & n2 . Now here n1≠ k n2  , where k…

Q: Question 3. Do the lines x=t, and x = 2t - 2, y = 2t - 1, 2 = 3t+1 intersect each other at only one…

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Q: Consider the two points P1(-1,2) and P2(1, 3) in the xy-plane. Question 14: 1. Find the distance D…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Consider the given diagram, find: (a) The coordinates of point R. (b) The exact distance from S to…

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Q: Question 13 Which of the following is an equation of a plane surface? O 222 + 3y + 4z = 4 O 2z2 +…

A: Equation of pane surface. Will be of the form ax+by+cz =d

Q: Consider the following. Зx + 2у + 62 3 36 Sketch a graph of the plane.

A: 3x+2y+6z=36 To find x-intercept, put y=0 & z=0, we get 3x+20+60=36⇒3x=36⇒x=12 To find…

Q: 6) Consider the plane P: z+y-2:= 0 in R³ that contains the point P₁(1, 1, 1). Answer the following…

A: As per the question we are given the plane P and a point P1 on it. Now we have to find the…

Q: which of the following is not created when a plane slices through a cone? A: Point B: Rectangle…

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Q: Question 1 of 40 What is the shape of the cross-section formed when a cylinder intersects a plane as…

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Q: Question 11 The equation x2 + 4y2 = 4 in three-dimensional space is an equation of %3D which…

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Q: Given points P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) find the parametric equation of the line PQ…

A: Here given point  P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) So  PQ=2-4, 5--2, 5-5=-1, 7, 0 PR=0-4,…

Q: Consider the plane shown in the following figure: Let 4, b, c, d 40. A general equation…

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Q: Problem 7 Find the distance from the point to the plane. (1) (6,0, –6), x – y = 4 (2) (3,0, 10), 2r…

A: Find the distance from the point to the plane. (1).   (6,0,-6) , x-y=4 We know that,   The distance…

Q: Question 4. Find an equation of the line of intersection of the planes -x+2y+z= 1 and x+y+z=0.

A: This is a problem related to geometry. Based on the general formula and concept we will answer the…

Q: Find an equation of the sphere that passes through the origin and whose center is (6, – 6, 3). OA.…

A: We will find the equation of sphere as following.

Q: Question 22 Consider the plane T:r-z= 1 and the line 2 3 + -1. Find the equation of the plane that…

A: Solved below

Q: QUESTION 2 Plot the surfaces given by: y = Vx? +z? .2 x² + y? - 3+ z? =0 X = 0 in one 3D-space.…

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Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

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Q: Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (1) What is the equation of the sphere…

A: Answer