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Someone please explain these!

The angle between two planes is defined as the angle between their normals. Determine the angle theta between 0 and 90 degrees between the given planes.

a) 2x+3y-z+9 = 0 and x+2y+4 = 0


If the positive z-axiz points up, show that the line x=0, y=t, z=2t is parallel to and below the plane 2x-10y+5z-1 = 0.

Find an equation for the set of points P(x,y,z) that are equidistant from the points A(1,2,3) and B(4,0,1)

  • Math -

    Love these kind of questions.

    1. normals are (2,3,-1) and (1,2,0)

    a∙b = │a││b│cosß

    2+6+0 = (√14)(√5)cosß


    ß will be the angle between the normals, can you take it from here?

    2. The line has direction (0,1,2) and the plane has a normal of (2,-10,5)

    take the dot product.
    If the normal is perpendicular to the line, shouldn't the line be paralle to the plane?

    3. vector AB = (3,-2,-2)
    this would be a normal to the plane, so the equation of the plane is

    3x - 2y - 2z = C

    Shouldn't this plane pass through the midpoint of AB ??

    I am sure you can take it from there.

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