Find two unit vectors that are parallel to the xy plane and perpendicular to the vector [1,-2,2].
To find unit vectors that are parallel to the xy plane, you can simply use the i and j unit vectors, which lie on the x-axis and y-axis respectively. These two unit vectors are already parallel to the xy plane.
Yes, any two unit vectors that are perpendicular to each other will be parallel to the xy plane. This means that as long as the i and j unit vectors are not in the same direction, they can form a pair of unit vectors that are parallel to the xy plane.
The direction of the unit vectors parallel to the xy plane is determined by the orientation of the x-axis and y-axis. The i unit vector points in the positive direction of the x-axis, while the j unit vector points in the positive direction of the y-axis.
Yes, unit vectors parallel to the xy plane can have different magnitudes. The magnitude of a unit vector only indicates the direction it is pointing in, not its length. As long as the unit vector is perpendicular to the xy plane, it is still considered to be parallel to it.
Unit vectors parallel to the xy plane can be used in vector operations such as addition, subtraction, and scalar multiplication. They can also be used to represent the direction of a vector in the xy plane by multiplying them by the magnitude of the vector.