A point P(1, 3, -5) is translated by 2î + 3ˆk

A point P(1, 3, -5) is translated by 2î + 3ˆk + 4ĵ and then rotated counter clockwise by 90° about the z-axis. The new position of the point is:

P = (1, 3, – 5)
First translated by 2î + 3ĵ - 4ˆk and them rotate about z – axis by 90°
Homogeneous Translation Matrix

Then rotated about Z – axis.