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Math Help - Acute angle between a plane and y axis

  1. #1
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    Acute angle between a plane and y axis

    Hey guys. The question goes like this :

    Coordinates of A(-1,2,5) and B(2,-2,11). Plane p passes through B and is perpendicular to AB. It is required to find
    (a) Equation of plane p
    (b) Acute angle between plane p and y axis.


    An equation for p is 3x - 4y + 6z = 80

    What is the next step to calculate the angle ?

    i use the formula cos θ = A . B / |A| x |B| ,

    i can substitute the value of A with normal vector of plane p. Then how should i proceed? Is there a direction vector for the y axis ??

    Thanks in advance




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  2. #2
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    Re: Acute angle between a plane and y axis

    Quote Originally Posted by nks2427 View Post
    Hey guys. The question goes like this :
    Coordinates of A(-1,2,5) and B(2,-2,11). Plane p passes through B and is perpendicular to AB. It is required to find
    (a) Equation of plane p
    (b) Acute angle between plane p and y axis.
    An equation for p is 3x - 4y + 6z = 80
    What is the next step to calculate the angle ?
    Given a plane N\cdot(R-P)=0 and line Q+tD if the line is not parallel to the plane, i.e. N\cdot D\ne 0, then the acute angle between the line and the plane is the complement of the acute angle between D~\&~N.

    In this case D=<0,1,0>~\&~N=<3,-4,6>.
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  3. #3
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    Re: Acute angle between a plane and y axis

    can D be taken as D = < 0, 2 , 0 > ?
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    Re: Acute angle between a plane and y axis

    Quote Originally Posted by nks2427 View Post
    can D be taken as D = < 0, 2 , 0 > ?
    Yes. Any vector parallel to the y-axis.
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  5. #5
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    Re: Acute angle between a plane and y axis

    Thank you D
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