2. The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = (v1, v2, V3) hasparametric equationsx = xo + tV1,y = Yo + tv2,z = 20 + tv3,-0

Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Answered: The line in R³ through the point Po(xo,…

The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations (vı, v2, V3) has x = x0 + tv1, y = Yo +tv2, z = 20 + tv3, -0

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 2E

See similar textbooks

Related questions

Q: Find the vector and parametric equations for the line through the point P(4, -2, -4) and parallel to…

A: Find the vector and parametric equations for the linethrough the point P4,-2,4 and parallel to the…

Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

Q: 2 7 Find the projection of v = -1 onto the line tlof R'Igiven by the parametric equation e = tul…

Q: Find the real number a such that the line of x = 1, y = 2-1, z=3+t, the plane of equation parametric…

A: Given parametric equations are x=t , y=2-t, z=3+t Where t∈ℝ and Plane is αx+5y+z-10=0

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

Q: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

Q: Express the given parametric equations of a line using bracket notation and also using i. j. k…

Q: The planes 4x + 4y + 3z = -15 and y - 5x - 2z = 11 are not parallel, so they must %3D intersect…

A: Given: The planes 4x+4y+3z=-15 and y-5x-2z=11

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

Q: 2. The line in R³ through the point Po(xo; Yo, 2o) and parallel to the vector v = parametric…

A: NOTE:- By bartleby rule, only question number (2) has been answered. The line in ℝ3 through the…

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

A: Given query is to find the equation of the line.

Q: Find parametric equations representing the line segment joining P(-4, 1) to Q(3, –2) as (æ(t),…

A: We have to find parametric equations to represent the line segment from P(-4,1) to Q(3,-2).

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t y…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is x =…

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: What is the parametric equations of line line through the point (1,2,-1)and is perpendicular to the…

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find the vector and parametric equations for the line through the point P(-5, 3, -1) and the point…

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

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that, Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: The objective is to find the parametric equations of the line through the point.

Q: Find the vector and parametric equations for the line through the point P = (-4, –4, 5) and the…

Q: Derive the parametric equations of the line of intersection of the two planes: II : 2x – y + 2z = -1…

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

Q: Find the vector parametric equation of the line that passes through the points P(6,–2, –1) and…

A: The vector equation of a line is . Where represent the position vector, represent the direction…

Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

Q: Eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint. 2 x2 + y2 = 36 x2…

A: We have to eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint.

Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

A: Let's find.

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1: x=1+t, y=1+6t, z=2tLine L2: x=1+2s, y=5+15s, z=-2+6s

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

Q: Express the given parametric equations of a line using bracket notation and also using i. j.k…

Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1: x−2y+z=1P2: 2x−2y−4z=4

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

2. The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = (v1, v2, V3) has
parametric equations
x = xo + tV1,
y = Yo + tv2,
z = 20 + tv3,
-0 <t < ∞.
(a) Show that we can rewrite the parametric equations without t as
- xo
Y – Yo
Vị
V2
V3
as long as v1, v2 and v3 are nonzero. These are known as the symmetric equations for the line
L.
(b) We can write the symmetric equations as two distinct equations:
x – x0
Y – Yo
y – Yo
z – 20
and
V1
V2
V2
V3
What kind of geometric objects in R³ do these two equations separately represent?
(c) Let L1 be the line through the point (xo, Yo, zo) = (1,0, –2) and parallel to v = (-1,3, 2).
Following the reasoning of (a) and (b) above, find two planes in R³ such that Li is their
intersection.
(d) Let L2 be the line through (x0, Yo, zo) = (1,0, –2) and v = (-1,3,0). Taking note that now
V3 = 0, find two planes in R such that L2 is their intersection.

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

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector-valued Function$

Learn more about

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