We present results from deep (70 ks) Chandra ACIS observations and Hubble Space Telescope ACS F475W observations of two highly optically polarized quasars belonging to the MOJAVE blazar sample, viz., PKS B0106+013 and 1641+399 (3C345). These observations reveal X-ray and optical emission from the jets in both sources. X-ray emission is detected from the entire length of the 0106+013 radio jet, which shows clear bends or wiggles - the X-ray emission is brightest at the first prominent kpc jet bend. A picture of a helical kpc jet with the first kpc-scale bend representing a jet segment moving close(r) to our line of sight, and getting Doppler boosted at both radio and X-ray frequencies, is consistent with these observations. The X-ray emission from the jet end however peaks at about 0.4 (~3.4 kpc) upstream of the radio hot spot. Optical emission is detected both at the X-ray jet termination peak and at the radio hot spot. The X-ray jet termination peak is found upstream of the radio hot spot by around 0.2 (~1.3 kpc) in the short projected jet of 3C345. HST optical emission is seen in an arc-like structure coincident with the bright radio hot spot, which we propose is a sharp (apparent) jet bend instead of a terminal point, that crosses our line of sight and consequently has a higher Doppler beaming factor. A weak radio hot spot is indeed observed less than 1 downstream of the bright radio hot spot, but has no optical or X-ray counterpart. By making use of the pc-scale radio and the kpc-scale radio/X-ray data, we derive constraints on the jet Lorentz factors (Gamma_jet) and inclination angles (theta): for a constant jet speed from pc- to kpc-scales, we obtain a Gamma_jet of ~70 for 0106+013, and ~40 for 3C345. On relaxing this assumption, we derive a Gamma_jet of ~2.5 for both the sources. Upper limits on theta of ~13 degrees are obtained for the two quasars. (ABRIDGED)
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