1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector Products & Properties

  1. Jan 16, 2009 #1


    User Avatar

    1. The problem statement, all variables and given/known data

    Which of the following are true?
    A) A vect. prod. C=C vect. prod. A
    B) The x-component of a vector can be +, -, or zero
    C) If A=BxC and C=64i, then Ax=0
    D) If A perp to B, then B dot A =0
    E) The magnitude of a vector is sometimes negative.
    F) The scalar (or dot) product of two vectors can be +, -, or zero.

    2. Relevant equations

    BxC = BC*cos(theta) where theta = angle between vectors

    3. The attempt at a solution
    Below are my attempts at proving or disproving each statements.

    A) False: Using the right hand rule, the direction of the resulting product will be inverted when comparing AxC and CxA
    B) True: A vector could cover horizontal distance to the right (positive), to the left (negative), or be a vertical vector with an x component of zero.
    C) False: 64i could potentially result in an answer where Ax = 64i
    D) True: BxA = BAcos(90) = BA*0 = 0
    E) False: A magnitude is the absolute value of a vector and therefore can never be negative.
    F) False: A scalar product must always be positive as all scalars are positive--they would be the absolute value of a vector.

    I tried answering B & D as true and the rest false but this was not correct. I am not sure which statements I am confused on. I'm fairly confident of my answers to A, B, D, and E while a little less sure on C and F.

  2. jcsd
  3. Jan 16, 2009 #2


    User Avatar
    Homework Helper

    C)Since A=BXC. A is perpendicular to B and C. Since C = 64i is along x axis, Ax is zero.
    F) A.B = ABcos(theta). ANd cos(theta) can be +, - or zero.
  4. Jan 16, 2009 #3
    To emphasize more about F)

    define 2 vectors A = (-1, 1) and B = (1, -1)

    [tex] A \cdot B = -1 - 1 = -2 [/tex]

    Certainly negative.
  5. Jan 16, 2009 #4


    User Avatar

    Thanks for the replies! C definitely makes sense when using the right hand rule. For some reason I was still relating Ci to Ax without thinking that they were perpendicular. As for F I see what they are asking for--I guess I was thinking that scalar had to mean magnitude but in actuality they just meant dot product.

    Thanks for the help,

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook