Find parametrizations for the lines in which the planes in Exercises 61–64 intersect.

61. x + y + z = 1, x + y = 2

62. 3x - 6y - 2z = 3, 2x + y - 2z = 2

63. x - 2y + 4z = 2, x + y - 2z = 5

64. 5x - 2y = 11, 4y - 5z =-17

### Want to see the full answer?

Check out a sample Q&A here*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: In Exercises 39-48, find a parametrization of the curve. 39. The vertical line passing through the…

A: Given: Vertical line passes through the point (3,2,0)

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

A: Click to see the answer

Q: Find a parametrization of the line passing through (2, 0, 4) and (4, 1, 2). r(t) =

A: Click to see the answer

Q: Write a parametrization for the straight line path from the point (3,3, 4) to the point (5, 2,-4).…

A: Click to see the answer

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y<=2, that lies above the…

A: Click to see the answer

Q: find a parametrization for the curve. 1. the line segment with endpoints (-1, -3) and (4, 1)

A: Click to see the answer

Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

A: Click to see the answer

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure

*question_answer*

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

A: Solution of the system of equation will give the equation of the line of intersection.

*question_answer*

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. P 1(7, 2, 4) and P…

A: Click to see the answer

*question_answer*

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Click to see the answer

*question_answer*

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Modify the given figure as shown in Figure 1.

*question_answer*

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

A: Click to see the answer

*question_answer*

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

A: Click to see the answer

*question_answer*

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point 3 , 2 , 0

*question_answer*

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

A: Click to see the answer

*question_answer*

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

A: Click to see the answer

*question_answer*

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

A: Click to see the answer

*question_answer*

Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Given point A (1,0,2) Plane 3x+y+z=9

*question_answer*

Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

*question_answer*

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: Click to see the answer

*question_answer*

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v, 3 - u cos v + u sin v) Where u € [0, 1] v€ [ 0,2π]

*question_answer*

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

A: Click to see the answer

*question_answer*

Q: Does the plane x = 5 have a trace in the yz-plane? Explain

A: To check whether the plane x=5 has a trace in the yz-plane or not. When we consider the equation x=5…

*question_answer*

Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain

*question_answer*

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

*question_answer*

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2, x + y - 2z = 5 The Arbitrarily set z =1 and solve the…

*question_answer*

Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

*question_answer*

Q: Find a parametrization of the line in which the planes x- 2y + 2z = - 1 and – 4x+ 3y – 3z = -1…

A: Click to see the answer

*question_answer*

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

*question_answer*

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

*question_answer*

Q: Find a parametrization of the line in which the planes x- 2y - 4z=1 and - 2x +3y + 6z = - 3…

A: Click to see the answer

*question_answer*

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

*question_answer*

Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

A: Click to see the answer

*question_answer*

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

*question_answer*

Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

*question_answer*

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

A: Click to see the answer

*question_answer*

Q: Find a parametrization of the line through the origin whose projection on the xy-plane is a line of…

A: Click to see the answer

*question_answer*

Q: Calculate fc((3x + 5y) i + (3x + 4y) j) - dr where C is the circular path with center (a, b) and…

A: According to the greens theorem:

*question_answer*

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

*question_answer*

Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

*question_answer*

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…

A: Parameterization of a curve: Parameterization of a curve in xy plane is a process of rewriting the…

*question_answer*

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

A: Click to see the answer

*question_answer*

Q: Let C be an ellipse in a horizonal plane lying above the xy-plane. Which type of quadric surface is…

A: Given, Let C be an ellipse in a horizontal plane lying above the xy-plane.

*question_answer*

Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,- 1)? A. x =…

A: A line connecting the points x1,y1,z1 and x2,y2,z2 can be calculated as,…

*question_answer*

Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…

A: Click to see the answer

*question_answer*

Q: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

*question_answer*

Q: Find the distance from the point Q(6, -2, 4) to the plane 2x - y + 2z = 4.

A: It is given that a point Q6,-2,4 and equation of the plane 2x-y+2z=4. Here, x1=6, y1=-2, z1=4 and…

*question_answer*

Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

A: Click to see the answer

*arrow_forward*

*arrow_forward*

*arrow_forward*

*arrow_forward*

*arrow_forward*

*arrow_forward*

*arrow_back_ios*

*arrow_forward_ios*