(a) Find parametric equations for the line through (4, 5, 4) that is perpendicular to the plane x − y + 2z = 6. (Use the parameter t.) (x(t), y(t), z(t))= ? (b) In what points does this line intersect the coordinate planes? xy plane = ? yz plane = ? xz plane = ?

(a) Find parametric equations for the line through (4, 5, 4) that is perpendicular to the plane x − y + 2z = 6. (Use the parameter t.) (x(t), y(t), z(t))= ? (b) In what points does this line intersect the coordinate planes? xy plane = ? yz plane = ? xz plane = ?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 36E

See similar textbooks

Related questions

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

Q: 10 + x 8 10 -10 –8 -6 -4 -2 4 6 -2 -4 -6 -8 -10- Which of the following sets of parametric equations…

Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

Q: Q/ Find the parametric equation for the line through the point (0, 1, 2) that is perpendicular to…

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

Q: 0 M) Find the point at which the line with parametric equations X=2+31, y=-41, z z =5+1 intersect…

A: Given: x=2+3t y=-4t z=5+t plane 4x+5y-2z=18

Q: 2. In the parametric equation, x = 2t, y = 3t 1, fill the table below. t 0 1 2 3 4 5 X x = 2t y y =…

Q: 2. Find the parametric equations of the line passing through the point (-1,4, –3) and is parallel to…

A: Given information is as below: r0=(-1,4-3)v=5i-j=(5,-1,0)

Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

Q: 31. (a) Show that the parametric equations x = x, + (x2 – x1)t y = yı + (y2 – yı)t where 0 <t< 1,…

A: Given data: The first parametric equation is x=x1+(x2-x1)t. The second parametric equation is…

Q: The parametric equation of the line through the origin that is parallel to the line given by x = t,…

Q: Find parametric equations for the line through the point (0, 2, 3) that is perpendicular to the line…

Q: Q1) Write the parametric equations of the line of intersection of the planes 2x-y+z 5 Note: Consider…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Here we have to find the equation of the tangent line.

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric…

Q: -10 -8 -6 -4 -2 6 8 10 -10+ Which set of parametric equations represents the curve shown in the…

A: According to the graph , we have

Q: 1. Find the parameter λ in the parametric form of the line l z+2 6:2-3-9-1-2-20 l: = X y so that…

Q: a)Find the equation of the tangent line to the curve and find a set of parametric equations for the…

A: To find the tangent equation of the line to the curve of intersection of both the given surfaces at…

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

Q: L0. Find parametric equation of the line perpendicular to the lines 11: x = 1-1, y=t, z= 2t -1 and…

Q: find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Find parametric equations for the line through the point, that is parallel to the given plane, and…

A: given point 0,2,2 given plane x+y+z=3 given line x=1+t,y=2-t,z=2t

Q: (a) Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A cartesian equation of the parametric curve x = 6t + 11E - 10, y = E is O A No solution OB.…

Q: 18. Find the acute angle between the plane x+2y-z=8 and the line with parametric equations x =1, y…

Q: 74. Determine the parametric equations for the line perpendicular to L:r = (5,6) + s(1,-s). ,sER…

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Q.1 Find the parametric equation of the line that 2)Passes point (1,3,7) and orthogonal to xy-…

Q: 2. Find the parametric equations of the line passing through the point (-1,4, -3) and is parallel to…

Q: Find parametric equations for the line through the point (0, 2, 2) that is perpendicular to the…

Q: Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle…

Q: 24) Consider line L of parametric equations x =t, y = 2t, z = 3, t E R. a. Find parametric equations…

A: The given line is: x=t, y=2t, z=3 and t∈R Now, consider the angle θ between two intersecting plane,…

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line (x-4) = 2…

A: The solution is given below in the next step:

Q: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: 3-12 Find an equation for the tangent plane and parametric equations for the normal line to the…

A: The surface F: x2y-4z2+7=0 and P-3,1,-2. Then we have to find the equation of the tangent plane and…

Q: O Given two points P(6,3,1) and Q(5, 0,0), find the parametric equations for a smooth curve, C:x =…

Q: 22. Find (a) parametric equations for the line of intersection, and (b) the cosine of the angle…

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: Find parametric equations for the line tangent to the curve of the intersection of the surfaces x +…

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

A: Given parametric equations, x=et,y=e3t+4 To find y.

Q: 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for…

A: The given parametric equations are,

Q: (a) Find parametric equations for the line through (5, 2, 4) that is perpendicular to the plane x -…

A: answer is in next step.

Q: (A) Find the parametric equations for the line through the point P = (-3, 4, -2) that is…

A: the parametric equation of a line passing through the point (x1,y1,z1) and having direction ratio…

Q: Find a set of parametric equations for the curve of intersection of a paraboloid x² + (y − 2)² = z…

Q: Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric…

Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

Q: 2. Find the parametric equations of the line through (0, 3) that is parallel to the line x= -5 + t y…

Q: Q. Find parametric equation of the line perpendicular to the lines l1: x = 1- 1, y=t, 12 : z = 2t –1…

Q: (3) Find parametric equations for the line of intersection of the planes. x + y - z = 2 and y + z =…

A: Given equation of the planes are x+y-z=2 y+z=0 we rewrite them as x+y-z-2=0, and 0x+y+z=0…

Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

A: Topic - equation of line

Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

(a) Find parametric equations for the line through (4, 5, 4) that is perpendicular to the plane x − y + 2z = 6. (Use the parameter t.)

(x(t), y(t), z(t))= ?

(b) In what points does this line intersect the coordinate planes?

xy plane = ?

yz plane = ?

xz plane = ?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Trending now

This is a popular solution!

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find a parametric equation of a line that passes through the point (1,3,-4) and is perpendicular to the plane -2x+y-5z=1 a) x=-2+t, y=1+3t, z=4+5t b) x=1-2t, y=3+t, z=-4-5t c) -2(x-1)+(y-3)-5(z+4)=0 d) (x+2)+3(y-1)-4(z+5)=0
Find parametric equations for the line through the point, that is parallel to the given plane, and perpendicular to the following line. (0, 2, 2)x + y + z = 3x = 1 + t, y = 2 - t, z = 2t x = 3s y = ? z = ?
Find a parametric equation for the line through the point (−7,4,−7) and perpendicular to the plane 7x+4y+9z=5 which is written using the coordinates of the given point and the coefficients of x, y, and z in the given equation of the plane.
(A) Find the parametric equations for the line through the point P = (-2, 5, -3) that is perpendicular to the plane 3x−1y+2z=1.Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. x = y = z = (B) At what point Q does this line intersect the yz-plane? Q = ( , , )
a) Find the parametric equations for the line in which the planes x-2y+4z=2 and x + 2y - 2z = 6 intersect. b) Find the parametric equations for the line which passes the point P (-1,0,3) and perpendicular to the plane 3x-7y+5z=21
Find parametric equations for the line through Po= (3, -1, 1) perpendicular to the plane 3x + 5 y - 1 z = 29.
Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane x+ y + z = 10 and perpendicular to the line x = 3 + t, y = -18 - t, z = 5t.