There was a triangle and he had a normal, but once the normal changed him and began to look in another direction, on a completely different vector.

I burned the triangle 1ms and decided also to turn so that they healed as before.

Task:
How to rotate the triangle to its normal? What would they live long and perpendicular?

  • 3
    There are infinitely many centers around which you can make a turn. For each will be your result. - AnT
  • And also infinitely many angles of rotation around the axis of rotation directed along the normal. - Kromster

1 answer 1

  • choose the zero vertex of the triangle A for the base point
  • we postpone from it an arbitrary vector perpendicular to the new normal and with the length of the vector AB
  • calculate the vector AD, perpendicular to N and AB ', as their vector product
  • find the vector AC 'as a linear combination of AB' and AD, providing the desired length AC and angle AC'B '

For other options, the statement of the problem does not provide enough data.

  • the author gave a reasonable idea, and the triangle began to live and be happy. Thank. - FatherOfFiveChildren