Calculus

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5. Determine an equation for the plane that is exactly between the points A(-1, 2, 4) and B(3, 1, -4).

  • Calculus -

    I assume the plane needs to pass through the mid-point between the two points, and perpendicular to the line joining the two points.

    First find the mid-point by
    M((x1+x2)/2,(y1+y2)/2,(z1+z2)/2)

    The normal vector for the plane is just the vector AB, or N(3-(-1),1-2,-4-4)=(4,-1,-8).
    The equation for the plane is then:
    4(x-xm)-(y-ym)-8(z-zm)=0
    where M(xm,ym,zm) as calculated above.

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