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can anyone explain vectors, line & plane equations and perpendicular stuff... watch

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    I'm lost as far as vector equations of planes and lines and their perpendiculars etc. are concerned... can anyone help?
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    perpendicular means when the vectors are at right angles to each other

    e.g

    r = i + j + k + µ[i + 2j + 3k]

    you see this bit µ[i + 2j + 3k]

    this is the direction vector, use this in the dot product with another direction vector to see if the vectors are perpendicular or not [dot product should = 0]
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    (Original post by lesser weevil)
    I'm lost as far as vector equations of planes and lines and their perpendiculars etc. are concerned... can anyone help?
    Lines usually have equations r=A+tB. A is any position vector which the plane passes through and B is the directional vector of the plane. t is a scalar parameter that can change to give different points on the line.

    Planes are a surface with infinite width and length, zero thickness and no curvature.
    In order to find any point on a plane you need to know an arbitrary point on the plane and 2 vectors in the plane, but not parallel to each other.
    The equation of a plane is most commonly written in the form r.n=a.n, where r is any point, n is a vector perpendicular to the plane and a is a known point in the plane. This equation stems from (r-a).n=0, as (r-a) is a vector in the plane, n is perpendicular and thus the scalar product is 0 as θ=90° and so cosθ=0
    The equation of a plane can be written in the form R=A+\lambdaB+tC, where A is any point on the plane, B and C are the non parallel vectors in the plane and \lambda and t are scalars.
    You can find a vector perpendicular to the plane by finding the vector product of two direction vectors in the plane (remember AxB gives a vector perpendicular to A and B).

    If there's anything more specific or any questions you're stuck on then feel free to ask.
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    so say you have a position vector A = ai + bj +ck and a direction vector B = di + ej + fk parallel to the line L going through A. How would you find an equation of L?

    And how would you calculate the acute angle between OA and L?
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    (Original post by lesser weevil)
    so say you have a position vector A = ai + bj +ck and a direction vector B = di + ej + fk parallel to the line L going through A. How would you find an equation of L?
    The equation of L is simply: r=(ai+bj+ck)+\lambda(di+ej+fk).
    \lambda is simply a variable parameter that takes different values to give different points on the line.

    And how would you calculate the acute angle between OA and L?
    You'd use the scalar product.
    OA has direction ai+bj+ck.
    L has direction di+ej+fk.
    (OA).(L)=[OA][L]cosθ
    ad+be+cf=\sqrt{a^{2}+b^{2}+c^{2}}\sqrt{d^  {2}+e^{2}+f^{2}}cosθ
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