Explain how the direction vectors of two lines in ℝ3 can be used to determine whether the two lines are parallel or identical. If the two lines are not parallel or identical, what are the possibilities for them?

Explain how the direction vectors of two lines in ℝ3 can be used to determine whether the two lines are parallel or identical. If the two lines are not parallel or identical, what are the possibilities for them?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 4EQ

See similar textbooks

Related questions

Q: If å = v2i +j - k, what is the vector whose alignment a is in the opposite direction and its size…

A: Given a→=2i+j−k We have to find the vector whose alignment a→ is in the opposite direction and its…

Q: What is the component form of the vector represented by 2a when a (-23)7

Q: How do you subtract two vectors algebraically? Geometrically?

A: Let the two vectors be a→ and b→. To find the difference between two vectors algebraically, that is…

Q: Determine whether or not the following pair of vectors are parallel, perpendicular or neither. a)…

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

Q: arry, an avid TikToker, decided to look at his faulty wristwatch to tell his friend dolphins the…

A: Given data on question: Length of hour hand , Lh = 3 cm Length of minute hand , Lm 1.5 cm Position…

Q: How do you know if 3 vectors span R^3? Is there any example?

Q: what will be the direction of -k x -i ?

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

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: Find the requested vector in R2 where A = (-3, 6), B = (8, –6) and C = (7,4). -2AB + 7CB = help…

Q: a) pair (4,-6) & (-6,9) b) pair (2,-3,1) & (4,-6,3) c) pair (6,-5,1) & (3,4,2)

A: To determine whether the following pairs of vectors are parallel, perpendicular or neither. a pair…

Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

Q: Write a vector equation for the line segment from P to Q. 4

Q: I used a vector to represent a wind velocity of 13 miles per hour from the west. Determine whether…

A: It is known that a vector is a quantity that has both a direction and a magnitude.

Q: How do you add two vectors algebraically? Geometrically?

A: Solution: Consider the two vectors: u→ = u1, u2 and v→ = v1, v2 Then the sum of u→ and v→is called…

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: If vector v is represented by an arrow, how is -3v represented?

A: Given: If vector v is represented by an arrow. To find: How is -3v represented?

Q: Write the vector equation that is equivalent to the system of equations: 12x1 13x2 11x3 14x1 2x2 6x3…

A: Simply write the each coefficient of x1 , X2 & x3 in each column respectively.

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: nd the vector that has the same direction as <3, -1, 4) but has length 52.

A: First find unit vector of direction then multiply with given magnitude

Q: Although I expected vector operations to produce another vector, the dot product of two vectors is…

A: The dot product of vectors is also known as scalar product of vectors. When we find dot product of…

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: b) How do you tell if two vectors are perpendicular?

Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

Q: What is a general equation for the line with vector equation x=[31]+t[4−5]

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: (a) How do you tell if two vectors are parallel?

Q: own your onw word, meaning for two vectors to be parallel?

A: Vectors are parallel if they have the same direction Both components of one vector must be in the…

Q: A vector is a ray that tells what direction True or false?

A: Given: A vector is a ray that tells direction. To determine: Whether the given statement is true or…

Q: Which of the following is a direction vector for the line through А (3, — 2) and В (1, 2)? Select…

Q: Write the vector and Cartesian (standard) equation of the line, given a point and slope below.…

A: Definition used - Vector equation of a line - r=a+λd Cartesian equation of a…

Q: of each pair of the given vectors -2 -4 6 -6 V2 -2 -1 2 8 7

Q: Ã = ë, + 3ểy – 2ể, : Calculate the angle between the B = 4ëx – ëy : vectors A* and B". = -3e, - 5ẽ,

Q: To find the dot product of two vectors, _________ corresponding components, andthen ____ these two…

A: To find the dot product of two vectors, _________ corresponding components, and then ____ these two…

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: (d) comp5 (e) projzā

A: Here we want to find component of vector b along the vector a . And Projection of vector a along…

Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

Q: Q2. What will be the effect of multiplying the vector by a positive and a negative scalar. Explain…

A: To find: The effect of multiplying a vector by a positive and a negative scalar. Explanation: When…

Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of B and C.

Q: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

Q: How do we know if two nonzero vectors are perpendicular?

A: Two non-zero vectors are perpendicular if their dot product is zero.

Q: What is the component form of the vector represented by 2a when = (-2, 3)? Enter the answer in the…

A: If we multiply by a constant to any vector then magnitude of that vector will be changed.

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: Find the vector form of the equation of the line in R2 that passes through P= (2, - 1) and is…

A: If a line is parallel to another line, then they have same slope.

Q: Harry, an avid TikToker, decided to look at his faulty wristwatch to tell his friend dolphins the…

A: Given data on question: Length of hour hand , Lh = 3 cm Length of minute hand , Lm = 1.5 cm…

Q: Perpendicular vectors are also said to be __________.

A: Perpendicular vectors are also said to be __________.

Question

Explain how the direction vectors of two lines in ℝ³ can be used to determine whether the two lines are parallel or identical. If the two lines are not parallel or identical, what are the possibilities for them?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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

$Projection$

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

We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.
If you were to translate the coordinates of point C using vector (-3,2) , what would the coordinates of the new point be?
The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is
Based on the graph, what would be the linear combination that will result in a zero vector?
How do we know if two nonzero vectors are perpendicular?
Suppose u= and v = are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are ...
(a) How do you tell if two vectors are parallel?
Why is the cross product of two vectors axb always equal a vector ?
The answer is B but how can I solve it by finding the directional vectors