You are observing a binary star system and obtain a series of spectra of the light from the two stars. In this spectrum, most of the absorption lines shift back and forth as expected from the Doppler Effect. A few lines, however, do not shift at all, but remain at the same wavelength. How could we explain the behavior of the non-shifting lines?

non-shifting lines indicate non moving star.

Explanation: when a star is moving toward the detector, the wavelength will decrease - there will be a blue shift.

When it's moving away from the earth or detector, the wavelength will increase - there will be a red shift.

Identifiable patterns of absorption lines that appear shorter or longer wavelengths than normal indicate that the star is moving

In visualisation, the bottom spectrum shows the normal position of absorption line for a star that is not moving toward or away from the earth.

no. dot product   =0 when vecs at right angles