How to find angle between line and plane?

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I have not done the computations, but I assume the issue is you can take two different vectors as the normal vector for the plane, and both works. Similarly you can take a different choice for the direction vector of the line. In practice one always choose the vector pairs such that the resulting angle is less or equal to 90 degrees. In your case the actual angle should be $$ 180-102.7=77.3 $$ and as a result the angle between the plane and the line should be $$ 90-77.3=12.7 $$ instead.

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Louzzy56
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Louzzy56

Updated on July 18, 2020

Comments

  • Louzzy56
    Louzzy56 over 3 years

    The normal of the plane is [-5,8,-14] and the direction vector of the line is [2,4,3]. I know that after using the equation cosθ=u⃗ ⋅v⃗ ||u⃗ ||⋅||v⃗ |, I must subtract 90º by the found angle in order to obtain the angle between the line and the plane.

    The issue I'm having here is that the angle between the normal and the line is about 102.7º. I know the angle between the plane and the normal is exactly 90º, so how is this possible? How can I go about finding the plane-line angle?

    • user84413
      user84413 over 9 years
      You can just subtract 90 degrees from your angle, or proceed as in the answer below.