The projection of a line segment of the z-axis on the x-axis is the length of the line segment.... State true or false and Justify
Projection is normally considered to be orthogonal.
The z-axis and x-axis are mutually orthogonal.
If a point or line (set of points) on the z-axis is projected (orthogonally) onto the x-axis, then that projection would be a single point at the origin.
Consider:
The length of the line P1P2 is given by d, where
d = √{(z2 – z1)^2 + (x2 – x1)^2}
Its projection onto the x-axis gives a line of length lx = x2 – x1.
If the line P1P2 now becomes a line segment of the z-axis by letting x2 = 0 and x1 = 0, then the length of P1P2 is d = z2 – z1.
But the length of its projection on the x-axis will be lx = 0 – 0 = 0
Hence, the statement is false.