1. An ultrasonic imaging apparatus comprising: ultrasonic transducer means, having a plurality of ultrasonic transducer elements arranged in a matrix having column and row lines, for emitting first and second ultrasonic beams to an object having a blood vessel extending in a predetermined direction therein and for converting echoes of the ultrasonic beams into first and second echo signals; driving means, coupled to said ultrasonic transducer means, for selectively driving said transducer elements for generating the first ultrasonic beam for scanning the object in a first B-scan orientation corresponding to the row lines, to obtain a first B-mode image, and the second ultrasonic beam for scanning the object in a second B-scan orientation corresponding to the column lines, to obtain a second B-mode image crossing the first B-mode image; means for designating a selected scanning position in the second B-scan orientation, the second B-mode image crossing the first B-mode image at the selected scanning position; means for converting, into first and second image signals corresponding to the first and second B-mode images, respectively, the first and second echo signals output from said ultrasonic transducer means, said first and second echo signals corresponding to the echo signals obtained by scanning the object in the first and second B-scan orientations, said converting means including means for detecting a Doppler component from the first image signal; and display means, coupled to said transducer means, responsive to the first and second image signals for displaying the first and second B-mode images.