NMAC BTWN A C172 TRAINING FLT IN LEVEL FLT AT 2500 FT UNDERNEATH CLASS B AIRSPACE AND A PIPER CHEROKEE IN LEVEL FLT XING IN FRONT OF THE C172. PLTS IN THE C172 DID NOT HAVE TIME TO REACT AND TAKE EVASIVE ACTION.

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AT THE ABOVE DATE AND TIME; I (PNF) WAS FLYING WITH A STUDENT PLT ON A NE HDG ENRTE TO SQL AT 2500 FT MSL. WE WERE MONITORING THE SQL TWR FREQ; BUT HAD NOT YET CONTACTED THEM. SUDDENLY; I OBSERVED A PIPER ACFT AT OUR 2 O'CLOCK POS AND 1/4 MI; AT OUR ALT; PROCEEDING W; R TO L. BEFORE I COULD TAKE EVASIVE ACTION; THE PIPER CROSSED IN FRONT OF US AND MISSED US BY ABOUT 250 FT! THE PIPER CONTINUED TOWARD HALF MOON BAY ARPT. I SWITCHED TO THE HAF UNICOM FREQ AND HEARD 'CHEROKEE; RPT 5 MI W OF HAF.' I HAD HIM IN SIGHT AND AM CERTAIN THAT WAS THE ACFT THAT PASSED ME. HE GAVE NO INDICATION; BY VOICE OR ACFT PATH; THAT HE EVER SAW US. THE PIPER APPEARED TO HAVE AT LEAST 2 PEOPLE ON BOARD; AND THE VOICE I HEARD WAS THAT OF A MALE. FRANKLY; I DON'T KNOW WHY I OR MY STUDENT DIDN'T SEE THE PIPER APCHING SOONER THAN WE DID. WE WERE LOOKING FOR OTHER ACFT AND NOT DISTR BY RUNNING A CHKLIST; TALKING ON THE RADIO; ETC. FURTHER; WE WERE IN SEVERE CLR CONDITIONS. I WILL HAVE TO INCREASE MY VIGILANCE IN LOOKING FOR OTHER ACFT AND TEACH MY STUDENTS TO ALSO DO SO.