Answered: Find a vector equation and parametric…

Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (2, 2.1, 3.1) and parallel to the vector 3i + 2j - k

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 8E: In vector form as in Exercises 5 and 6, find an equation for the line through the point 4,1,-3 and...

See similar textbooks

Related questions

Q: Find a parametric equation of the line M through p and q for the given values of p and q. [Hint: M…

Q: Use the properties of vectors to solve the following equations for the unknown vector x = (a, b).…

Q: Find the resultant force of two vectors F = 5î + 2j and F = -2î - 8j. Graph the two vectors as well…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: 10. A Plane is flying at 45 degrees north of the x axis at 400 mph. Sketch the situation and find…

A: Drawing the given data , Plane is at "A" From the diagram the x-component is OB…

Q: Find the distance of point A(23.2) from the line that passes through the origin and parallel to the…

A: given point A 23 ,2 and line passes through orgin and parallel to the vector v =<1,3>

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: nd an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given point P(2,6,-9) i.e. x1=2, y1=6 and z1=-9Given vector is n=j i.e. c=1We know that equation of…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given that point 2,6,-8 and vector or line ,n=jTo find : equation of plane Solution :Direction of…

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given that : P = ( 1, 0 ) and d = -13 .

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: Given the points P = (1, 5, –2), Q = (2, 3, –1) and R = (–4, 2, 5). 1. Find the vector that is…

A: Given points, P=1, 5, -2Q=2, 3, -1R=-4, 2, 5 The vectors are…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: Please answer the following question Find the vector equation of a line L going through the points…

A: Determine the direction vector m for the line L going through the points (-3,-1) and (-4,3).…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: We have to find the equation of plane.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: Which of the following equations correctly expresses the relation between vectors A, B, and C shown…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: The equation of the plane P which is normal to the vector n and passes through the point R is given…

Q: Rewrite the vector equation r(t) = (-2+ 4t)i+ (–1+t)j +(-1– 2t)k as the corresponding parametric…

A: Parametric equation of line in 3D

Q: A jet is flying through a wind that is blowing with a speed of 55 mi/h in the direction N 30° E (see…

Q: Q#2: a) Find the vector, parametric and symmetric equations for the line through the point (5,2,4)…

A: Solution is given below:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given: (2,3,-6) Perpendicular to j vector

Q: find an equation for the line through P perpendicular to v. Then draw a sketch of the line,…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Topic = Geometry

Q: Find a parametric equation of the line M through p and q for the given values of p and q. [Hint: M…

A: Handwriting solution

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is…

A: Solution....

Q: find the component form of the vector. The vector 5 units long in the direction opposite to the…

A: Given vector (3/5)i+(4/5)j is unit vecor as its magnitude is 1

Q: 4. Consider the points A(1, –1, 4), B(2, – 2, 5) and O(0, 0, 0). (a) Calculate the cosine of the…

A: The given points are A(1,-1,4) and B(2,-2,5) and O(0,0,0) The cosine of the angle between two…

Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

Q: Find the vector parametric equations for the line. in the direction of the vector 57-5-k and through…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

Q: Solve the following vector problems and parametric equations: a) Find the vector equation and the…

A: Q. Vector eqn of line passing through Prx0,y0,z0 and parallel to x, y , z is r = Pr +…

Q: Write the parametric equations for the given vector equation: [2 [x, y, z] = [11,2,0] + t[3,0,0]

Q: Consider the point P(-2,3) on the coordinate system. Describe geometrically the position vector…

A: Given point P (2,3)

Q: A jet is flying through a wind that is blowing with a speed of 45 mi/h in the direction N 30° E (see…

A: Since you have asked for a question with multiple sub-parts. We will solve first three parts for…

Q: snip1

A: The given point is, P=1,2,-1 which is parallel to the vector d=5-13. The objective is to find the…

Q: The position vector of a particle is r(t). Find the requested vector. The velocity at t = for r(t) =…

Q: nd he position vector in the form of xr+ yr for the vector that starts at the point (-1, 2), ends at…

A: Given query is to find the vector ,it's magnitude and direction.

Q: The points A and B have position vectors j+2k and 2i+j-2k respectively. (i) Find a vector equation…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: Rewrite the vector equation r(t) = (2+t)i + (1+3t)j + (-1+5t)k as the corresponding parametric…

A: We have to find the equation

Q: A:-Find parametric equations for the lines, the line through (4, 7, 1) perpendicular to the vectors…

A: I am attaching image so that you understand each and every step.

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, −1,…

A: Find a vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

Q: Sketch the vectors ro = and v= and then sketch the six vectors ro±v,ro ± 2v,ro± 3v. Draw the line L:…

A: Given the vectors r0=-1,2 and v=1,1. The objective is to compute the vectors r0±v, r0±2v and r0±3v…

Q: Find the distance of point A(2/3,2) from the line that passes through the origin and parallel to the…

Q: Find an equation of the plane passing through the given point and perpendicular to the given vector.…

A: Equation of a plane perpendicular to a, b, c and passing through x0, y0, z0 is, ax-x0+by-y0+cz-z0=0

Q: (6) Show that the vector equations r = -2i + j+ t(-į+ 5j) and r = -3i + 6j + s(-3i + 15j) | | refer…

A: The vector equation of a line is r⇀=a⇀+λb⇀. Where a⇀ and b⇀ represent the position vector and…

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

Find a vector equation and parametric equations for the line. (Use the parameter t.)
The line through the point (2, 2.1, 3.1) and parallel to the vector 3i + 2j – k
r(t) =
(x(t), y(t), z(t))

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

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

In vector form as in Exercises 5 and 6, find an equation for the line through the point 4,1,-3 and with the direction vector 1,2,3.
Find a vector equation and parametric equations in t for the line through the point and perpendicular to the given plane. (P0 corresponds to t = 0.) P0 = (4, 0, 9) x + 4y + z = 1
Find the parametric and symmetric equations of the line that passes through the point P(3, 0, -2) and is parallel to the vector v = 2i – j + 3k.
Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv = (4, -1, 4).Assume r(0)=4i−2j−4kr(0)=4i−2j−4k and that vv is the velocity vector of the line..r(t)r(t) = ii + jj + kk Rewrite this in terms of the parametric equations for the line. x = y = z =
. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line h3t−2, 2t+ 1, t+ 4i. Given both the vector equation and the parametric equation.
Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k
Find parametric equations for the lines in The line through the point P(3, -4, -1) parallel to the vector i + j + k
Rewrite the vector equation r(t) = (2+t)i + (1+3t)j + (-1+5t)k as the corresponding parametric equations for the line.
Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, −1, 2), Q( 1/2 , 1/3, 1/4)
Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u = i + 2j + 3k and v = 3i + 4j + 5k
Find a vector equation and parametric equations for the line through the point (4, 2.7, 3.1) and parallel to the vector 4i+2j-k r(t) = (x(t), y(t), z(t)) =
Solve the following vector problems and parametric equations:a) Find the vector equation and the parametric equation of the straight line on R3 running throughpoint � "(2,1, −3) and parallel to the vector v = (3, −2, 4).b) Use the equation obtained in a) to find 2 points on the line,which is not point P0.c) Use the equation again obtained in a) to test what the point is� (11, −5,9) and point � (14, −3,17) lie on this line