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Math Help - Proof of vectors

  1. #1
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    Proof of vectors

    this one problem on my practice sheet for my linear algebra test was confusing me, so i was wondering if anyone could show me how it is done in case i receive another problem like it...

    Given vectors v1, v2, v3, suppose that v1 = xv2 for some scalar x. Prove that if v2 is perpendicular to v3, then v1 is perpendicular to v3.
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  2. #2
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    Quote Originally Posted by faure72 View Post
    this one problem on my practice sheet for my linear algebra test was confusing me, so i was wondering if anyone could show me how it is done in case i receive another problem like it...

    Given vectors v1, v2, v3, suppose that v1 = xv2 for some scalar x. Prove that if v2 is perpendicular to v3, then v1 is perpendicular to v3.
    Two vectors a and b are perpendicular if a (dot) b = 0

    Now we know that v2 (dot) v3 = 0

    So v1 (dot) v3 = [xv2] (dot) v3 = x[v2 (dot) v3] = x[0] = 0.

    -Dan
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  3. #3
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    Hello, faure72!

    Two vectors u and v are perpendicular if and only if uv = 0.


    Given: vectors v1, v2, v3.
    Suppose that v1 = x(v2) for some scalar x.
    Prove that if v2 is perpendicular to v3, then v1 is perpendicular to v3.
    We are given: .v1 = x(v2) . . v2 = v1/x .[1]

    And we are given: .v2 perp v3 . . v2v3 = 0 .[2]

    Substitute [1] into [2]: .(v1/x)v3 .= .0 . . (v1v3)/x .= .0 . . v1v3 .= .0

    Since v1v3 = 0, then: .v1 perp v3.

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