×
Follow Us
Results 1 to 4 of 4

Vector Math format question

 Jump to latest post
    #1
  1. mcmahanrf is offline Junior Member Pro Subscriber
    Join Date
    Dec 2019
    Posts
    12
    Reputation

    Vector Math format question

    I got the question:

    a, b and c are three vectors such that c is perpendicular to both a and b. What is the value of a × b × c?
    a. (1, 1, 1)
    b. (0, 0, 0)
    c. (1, 1, 0)
    d. (0, 0, 1)

    can someone explain what this question is looking for? I have no idea what the answers even represent. It seems like there should be more information in this question to me

  2. #2
  3. Kalbi_Rob's Avatar
    Kalbi_Rob is offline Experienced Member Pro Subscriber
    Join Date
    Feb 2018
    Location
    Jacksonville, NC
    Posts
    290
    Reputation
    Quote Originally Posted by mcmahanrf View Post
    I got the question:

    a, b and c are three vectors such that c is perpendicular to both a and b. What is the value of a × b × c?
    a. (1, 1, 1)
    b. (0, 0, 0)
    c. (1, 1, 0)
    d. (0, 0, 1)

    can someone explain what this question is looking for? I have no idea what the answers even represent. It seems like there should be more information in this question to me
    a × b × c = 0

    Step-by-step explanation:

    Given that,

    • c and a are perpendicular to each other,

    then c * a = 0

    • c and b are perpendicular to each other,

    then c * b = 0

    Now, a × b × c

    = (a × b) × c

    = c × (a × b)

    = {(c * b)a - (c * a)b}

    = {(0)a - (0)b} = 0-0 = 0

    or known as vector point (0, 0, 0)

    https://tardigrade.in/question/if-a-...-then-vs3wj0g6

  4. #3
  5. Kalbi_Rob's Avatar
    Kalbi_Rob is offline Experienced Member Pro Subscriber
    Join Date
    Feb 2018
    Location
    Jacksonville, NC
    Posts
    290
    Reputation
    Quote Originally Posted by mcmahanrf View Post
    I got the question:

    a, b and c are three vectors such that c is perpendicular to both a and b. What is the value of a × b × c?
    a. (1, 1, 1)
    b. (0, 0, 0)
    c. (1, 1, 0)
    d. (0, 0, 1)

    can someone explain what this question is looking for? I have no idea what the answers even represent. It seems like there should be more information in this question to me
    That last post probably didn't help, so I'll direct you to our favorite website, Wikipedia:

    https://en.wikipedia.org/wiki/Cross_product

    Specifically look at the Definition equation:

    a x b = ||a|| ||b|| sin (@) * n

    where @ is the angle between a and b in the plane containing them (hence, it is between 0° and 180°)
    and n is a unit vector perpendicular to the plane containing a and b, in the direction given by the right-hand rule

  6. #4
  7. mcmahanrf is offline Junior Member Pro Subscriber
    Join Date
    Dec 2019
    Posts
    12
    Reputation

    found the easy way to intuit this answer

    Quote Originally Posted by Kalbi_Rob View Post
    a × b × c = 0

    Step-by-step explanation:

    Given that,

    • c and a are perpendicular to each other,

    then c * a = 0

    • c and b are perpendicular to each other,

    then c * b = 0

    Now, a × b × c

    = (a × b) × c

    = c × (a × b)

    = {(c * b)a - (c * a)b}

    = {(0)a - (0)b} = 0-0 = 0

    or known as vector point (0, 0, 0)

    https://tardigrade.in/question/if-a-...-then-vs3wj0g6

    I found an easy way to figure this out, also there is a small error in your description.

    The cross product function is not communitive so:

    = (a × b) × c

    = c × (a × b)

    is not true, it should be:

    = (a × b) × c

    = c × -(a × b)

    I'm not sure how you got the rest.



    /////This is what I said
    However, you don't need to do any of that because from the question we know that c is perpendicular to both a and b which means that a and b have to be parallel to each other.

    Since the cross product of parallel vectors is the zero vector then:

    A x B x C = 0 x C

    and since the cross product of a vector with the zero vector is also zero:

    0 x C = 0

    which is then written in coordinate notation as (0, 0, 0)

    //////This is what I realized

    So just because C is perpendicular to both A and B doesn't mean that A and B have to be parallel, they can be but they don't have to be. They can also be perpendicular to each other, they can also be somewhere in between. However in any case no matter how A and B are orientated to each other the cross product will be a vector extending 90 degrees from the plane they create together. The magnitude of this vector will vary based on the angle between them but it will always be 90 degrees offset from them.

    Now with that thought, we know that because the cross product must be done in order, we get:

    A x B x C == (a vector that is perpendicular to A and B) x (a vector we have already been told is perpendicular to A and B)

    and since these to vectors are both perpendicular to the same plane they MUST be parallel to each other. And then with the knowledge that the cross product of parallel vectors is zero we again get the correct answer of (0, 0, 0)
    Last edited by mcmahanrf; August 8, 2021 at 07:15 AM. Reason: realized something

Subscribe

Share this thread

Related Topics

  1. Phase to neutral equivalent math
    By randyw8483 in forum NETA Level 3 Exam
    Replies: 1
    Last Post: February 16, 2020, 04:20 PM
  2. Step up transformer vector group
    By Diarymh in forum Electrical Testing Talk
    Replies: 0
    Last Post: March 26, 2019, 06:23 AM
  3. Transformer Math Questions
    By david.hatch in forum NETA Level 3 Exam
    Replies: 4
    Last Post: October 10, 2018, 08:07 AM
  4. Transformer vector group test procedure
    By YugiGrobler in forum Electrical Testing Talk
    Replies: 0
    Last Post: November 27, 2017, 07:04 PM

Tags for this Thread

Follow us


Explore TestGuy


NETA Certification Training


NICET Electrical Power Testing


Help and Support




You are viewing the archives. Enjoy new features and join the conversation at wiki.testguy.net