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sintec
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How can I show that 2 lines lie in the same plane?
How can I get the equation of that plane?
Thanks!
How can I get the equation of that plane?
Thanks!
Originally posted by sintec
How can I show that 2 lines lie in the same plane?
How can I get the equation of that plane?
Thanks!
To determine if two lines lie in the same plane, we can use the cross product of the direction vectors of the lines. If the cross product is equal to the zero vector, then the lines are parallel and therefore lie in the same plane.
Yes, as long as the two lines are not parallel and do not intersect, they can lie in the same plane. This means that the two lines are coplanar.
The equation used to show that two lines lie in the same plane is called the scalar equation of a plane. It is given by ax + by + cz = d, where a, b, and c are the coefficients of the direction vector of the plane and d is a constant.
If the two lines do not have equations in the same form, we can rearrange the equations to match and then compare the coefficients. If the coefficients are equal, then the lines lie in the same plane.
Yes, another method is to find the point of intersection of the two lines. If the point lies on both lines, then the lines are coplanar. Additionally, we can also use the distance formula to calculate the distance between the two lines. If the distance is equal to 0, then the lines are parallel and therefore lie in the same plane.