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Scalar product

  1. Apr 23, 2014 #1
    Vectors a and b correspond to the vectors from the origin to the points A with co-ordinates (3,4,0) and B with co-ordinates (α,4, 2) respectively. Find a value of α that makes the scalar product a[itex]\cdot[/itex]b equal to zero, and explain the physical significance.


    My attempt:
    The scalar product a[itex]\cdot[/itex]b is given by |a||b|cosθ=[itex]5 \sqrt{α^{2}+20}[/itex]cosθ=0, therefore [itex]α=\sqrt{20}[/itex]i. But I don't know the physical significance of this. Please help!
     
  2. jcsd
  3. Apr 23, 2014 #2

    jbunniii

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    No, ##\alpha## is a real number, so you won't be able to achieve ##\sqrt{\alpha^2 + 20} = 0##. The solution you are seeking will give you ##\cos \theta = 0##. But since you haven't related ##\theta## to ##\alpha##, that doesn't help much. Instead of using ##a \cdot b = |a||b|\cos \theta##, do you know another formula for ##a \cdot b##?
     
  4. Apr 23, 2014 #3

    HallsofIvy

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    That is one way calculate the dot product but, rather than calculate [itex]\theta[/itex], it is simpler to use [itex](a, b, c)\cdot (u, v, w)= au+ bv+ cw[/itex]. Here that would be 3a+ 16+ 0= 3a+ 16= 0.

    No, a must be a real number. The fact that the dot product is 0 does NOT mean one of the vectors must have length 0. It is also possible that [itex]cos(\theta)= 0[/itex].

    Two non-zero vectors have 0 dot product if and only if they are perpendicular.
     
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