Question 22 Consider the plane T:r-z= 1 and the line 2 3 + -1. Find the equation of the plane that contains l1 and is orthogonal to 7. CS Scanned with CamScanner

Q: Question 1: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A)…

A: Given that L is the line of intersection of the planes 2x-y-3z=4 and 2x+y-z=2

Q: Question 22 Consider the plane n :r-z=1 and the line 2 Find the equation of the plane that cantains…

A: Explained below

Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

Q: Consider a, B, t/= 0. A possible graphical representation for the plane of equation Bx + ay +t = 0…

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Q: Consider the hyperboliode H defined by the equation:  x^2+y^2−z^2=1 and the point P0=(1,4,4) in H.…

A: We are given the following hyperboloid : x2 + y2 - z2 = 1 And we have to choose the correct…

Q: 4. •E D - Give two other names for AB. . Name three points that are collinear. -. Give another name…

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

Q: Show that the point P(4,-1,1) is common to the lines L, and L, Find The point of intersection of L2…

A: In this question, we find the intersection point and find the equation of plane containing lines.

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: Question 6. Find an equation for the plane which satisfies the given conditions. 1. Passes through…

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Q: Question # 4: Let and y = For what value(s) of h, is y in the plane generated by vi and va?

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Q: Question 3. Find the point of intersection of the lines ix=--1-t, and then find the plane determined…

A: We have to find the intersection point of the lines and equation of plane passing through these…

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: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: Question 19 Let L be the line passing through the point P-(-1, 2, 2) with direction vector d-[1,-2,…

A: First find the equation is line by given points and direction.  Then assume it T and convert (x,y,z)…

Q: Question 4 2 pts Find the point of the intersection of the plane P: 2х — Зу + 42+14- 0 and the line…

A: Given that  The plane and the line  To find the point of intersection of the plane and the line

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: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Let's solve.

Q: Let pi = (0,1, 0) and p2 = (2, –1,1). Give the equation for a line passing through Pi and P2, as…

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Q: Question 4 2 Let L be the line with the equation -3 +t 2 and let II 4 3 be the plane with equation…

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: Question 19 An equation of the line passing through the points P(2,3)P(2,3) and Q(3,8)Q(3,8) in the…

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Q: 6) Consider the plane P : x+y – z = 0 in K³ that contains both the points P1(1,0, 1) and P2(-1,1,0).…

A: Given : plane P : x + y - z = 0  & Points P1(1,0,1) & P2(-1,1,0) To find :  1. Equation of…

Q: Question 8 Find the equation of the plane that passes through the points A = (2,4, – 3), B =…

A: Plane problem....

Q: 2. Which of the following describes a different plane than the other three? (a) x + 2y + 3z = 6 (b)…

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Q: QUESTION 1 For the parametric line L: x =4+t, y y =3+t, z=D3+2t and the plane P: -y = x+ 2z + 2,…

A: Compute the direction ratios of both the line and the normal of plane.

Q: Question 8 An equation of the plane passing through the points A(1,2,3), B(2, 3, 1), C(3, 1,2) is…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

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 plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , .  Here, the points are .

Q: In computer graphics and perspective drawing, we need to represent objects seen by the eye in space…

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Q: 2. The plane with equation: 7 = (1,2,3) + m(1,2,5) + n(1,–1,3) intersects the y- and z- axes at two…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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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: Show the following curve is flat and Write the equation of the plane on which the curve is located:

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Q: b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the…

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Q: Di+Oj

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Q: QUESTION 1 For the parametric line L: x = 4+t, y = 3+t, z= 3-2t and the plane P: -y= x+ z + 2, then…

A: topic : line and plane line and plane are parallel to each other

Q: Consider the points P, Q and R with position vector (with respect to the origin O = (0,0,0)) d = (4,…

A: Given three points P Q and  R with position vectors a b and c. The solution to the three questions…

Q: QUESTION 10 The line L(t) = (-1+t,3-t,1-t) intersects the plane x - 2y-z=4 at the point P(2,0, – 2)…

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Q: Question 1: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1,…

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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: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: Exercises 7-10, sketch the plane curve by plotting points. Indicate the orientation of the curve.…

A: Consider the given parametric equations, x=t2-4 and y=t-1 on the interval -2≤t<2 find the…

Q: Given a plane T with equation x – y – z = -9 and a point Po = (1, –1,2). Find the shortest distance…

A: Given plane T : x-y-z = 9 Point P0 = (1,-1,2) To find →the shortest distance d from P0 to T…

Q: Two automobiles are driving on a plane. The first automobile is moving north at 10 m/s and rising 5…

A: Let's consider North as +ve y-axis, East as +ve x-axis, and upward motion to be +ve z-axis. Now, the…