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Vectors math! (confused)

  1. Feb 27, 2015 #1
    1. The problem statement, all variables and given/known data
    1. Verify (https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 + https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) × (https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-a.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117 + https://ucdsb.elearningontario.ca/content/enforced/4850117-BL_1415Sem2__MAT_MCV4UU-948314_1_ELO/MCV4UPU01/MCV4UPU01A06/images/vec-b.gif?_&d2lSessionVal=Y3hirJUTSYjH76OEZwqHIBATE&ou=4850117) = 0⃗ . What can be said about two vectors whose cross product is the zero vector


    a x b

    = i j k
    3 -3 1
    -12 12 -4

    =
    i
    ( (-3) · (-4) - 1 · 12 ) -
    j
    ( 3 · (-4) - 1 · (-12) ) +
    k
    ( 3 · 12 - (-3) · (-12) ) =
    =
    i
    ( 12 - 12 ) -
    j
    ( (-12) - (-12) ) +
    k
    ( 36 - 36 ) =
    =
    (0 ; 0 ; 0)

    2. Relevant equations


    have i correctly verified with an example that two vectors whose cross product is the zero vector?
     
  2. jcsd
  3. Feb 27, 2015 #2
    You have created two vectors with zero cross product. Do you understand what can be said about two vectors whose cross product is zero?
     
  4. Feb 27, 2015 #3

    They are parallel, since the cross product involves the cosine function. cos(90) = 0. The cross product is a sine function, if it is zero, the angle is zero or 180, so they are in the same or opposite directions. ???
     
  5. Feb 27, 2015 #4
    That's it, but the cross product is AB*sin(x). I'm not following what you meant by the line below, but you got the main point.

     
  6. Feb 27, 2015 #5

    Mark44

    Staff: Mentor

    No, that's not the cross product. What you're probably thinking of is |A| |B| |sin(θ|), which gives the magnitude of A X B.
     
  7. Feb 27, 2015 #6

    Mark44

    Staff: Mentor

    As already pointed out by jasonleroy, the cross product does NOT involve the cosine function. The cross product also does not involve the sine function, although the magnitude of the cross product does.
     
  8. Feb 27, 2015 #7
    then what would the cross product be ?
     
  9. Feb 27, 2015 #8

    Mark44

    Staff: Mentor

    Just what you already did with the "pseudodeterminant."

    $$\begin{vmatrix} i & j & k \\ x_1 & x_2 & x_3 \\ y_1 & y_2 & y_3\end{vmatrix}$$
     
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