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Math Help - [SOLVED] How to find vector of right triangle w/ 3 pts

  1. #1
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    [SOLVED] How to find vector of right triangle w/ 3 pts

    A (3,0,2)
    B (4,3,0)
    C (8,1,-1)

    How do i check to see if these are part of a right triangle and which vertex is the right triangle?

    I can find cross products and dot products and distances between points and point and a line, but I do not understand the wording of this problem. What must I do?
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  2. #2
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    Quote Originally Posted by thekrown View Post
    A (3,0,2)
    B (4,3,0)
    C (8,1,-1)

    How do i check to see if these are part of a right triangle and which vertex is the right triangle?

    I can find cross products and dot products and distances between points and point and a line, but I do not understand the wording of this problem. What must I do?
    Find vectors AB, BC, AC and take all three dot products.

    If any of them is 0, then you have a right angle.
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  3. #3
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    Alright so I found them:

    vectors:
    AB (1,3,-2)
    BC (4,-2,-1)
    AC (5,1,-3)

    dot products:
    AB.BC = 4-6+2 = 0 <---
    BC.AC = 20 -2 +3 = 21
    AB.AC = 5 + 3 + 6 = 14

    So to answer this question correctly, the vertex at which the right triangle is the dot product AB.BC?

    How do I formulate this in words... do I say "the vertex at which the right triangle is the dot product AB.BC"?
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  4. #4
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    Vector AB is from A to B. Vector BC is from B to C. What point of the triangle do those have in common?
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  5. #5
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    Ah I see it, so the point B, common to both, is the point where the angle is a right angle. Point B is the "corner" where the angle is 90 degrees.
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