If the direction vectors of a slant line and its projection on the plane are vector a = (1,0,1) and vector b = (0,1,1), then what is the angle between the slant line and the plane? Why there are two direction vectors and there is only one on the definite plane

If the direction vectors of a slant line and its projection on the plane are vector a = (1,0,1) and vector b = (0,1,1), then what is the angle between the slant line and the plane? Why there are two direction vectors and there is only one on the definite plane

Your understanding is wrong. What is the meaning of this topic
The direction vector of a diagonal line in the plane is a = (1,0,1)
The direction vector b = (0,1,1)
If the angle between the oblique line and the plane, that is, the angle between the oblique line and the projection, is set to x, then cosx = a * B / | a | B | = 1 / 2, x = 60 degrees
In addition, there are countless direction vectors of the same line. For example, the diagonal direction vector is vector a = (1,0,1). In fact, any vector collinear with vector a can be taken as the direction vector. Of course, this has nothing to do with the problem

Rectangular coordinate operation of vector
Translate the parabola F: y = x ^ 2-4x + 5 to vector a, make vector a and corresponding curve f '= y' = x '^ 2, and find the coordinates of vector a

Observe F: the axis of symmetry is x = - B / (2a) = 2, the ordinate of the lowest point is y = 2 ^ 2-4 * 2 + 5 = 1, the coordinate of the lowest point is: (2,1) the corresponding curve f ': the axis of symmetry is x = 0, the coordinate of the lowest point is (0,0), so the translation vector a is: (- 2, - 1)