Suppose you start at the origin, move along the x-axis 3 units. Then face downwards and move forward 4 units. Then turn right and move 7 units. Then (relative to your current position) face downwards and move forward 3 units. What are the coordinates of your position?
What I did using the description given:
step 1- move along the x-axis 3 units: $x=3$
2-Then face downwards and move forward 4 units: $x=3, z=-4$
3-Then turn right and move 7 units: $x=3, z=-4, y= 7$
4-face downwards and move forward 3 units: $x=3, z=-1, y= 7$
The point is (3,7,-1)
But the answer is wrong, how could I know the points from the description?
As I interpret this, you should also keep track of which direction you're facing, and what is your sense of "down". This is what I got:
Step one: Move along the $x$-axis: $(3, 0, 0)$, your face points in the positive $x$-direction, your feet point in the negative $z$-direction.
Step two: Face downwards, and move forwards $4$ steps: $(3, 0, -4)$, face is now in the negative $z$-direction, and feet are in the negative $x$-direction.
Step three: Turn right and move seven units: $(3, -7, -4)$, face is in the negative $y$-direction, feet are in the negative $x$-direction.
Step four: Turn down (relative to your current orientation) and move forward $3$ units: $(0,-7, -4)$, face in the negative $x$-direction, feet in the positive $y$-direction.