Bendix Corp. yesterday announced it has purchased more than $75 million in RCA Corp. stock, triggering a sharp, personal attack by RCA on Bendix Chairman William M. Agee. RCA charged that "Mr. Agee has not demonstrated the ability to manage his own affairs let alone someone else's."

Agee, whose unconventional leadership of Bendix has jolted the Detroit-based aerospace and automotive company, said the purchase of RCA stock was solely for investment purposes. "Our substantial purchase is a statement of confidence in RCA's future," Agee said. Under Securities and Exchange Commission regulations, Bendix was required to disclose its ownership of more than 5 percent of RCA stock. The exact amount was not disclosed, although Bendix said its total holdings are less than 9.9 percent.

But RCA shrugged off these soothing words to lash at Agee. It was unclear to what RCA was referring in attacking Agee's personal conduct. Last year, Agee made headlines because of a controversial relationship with Mary Cunningham, a former Bendix executive who left the company amid rumors that she and Agee were linked romantically.

RCA said that "Mr. Agee's actions in secretly accumulating a bloc of RCA stock show that his only purpose is to further his own ambitions and not the interests of RCA and its stockholders or even Bendix and its stockholders."

Agee met yesterday with Thornton Bradshaw, chairman of RCA, to inform him of Bendix' action and to assure him that it was a "friendly" move. Bendix is making "no requests for any changes or specific actions to the RCA management," Agee said.

But Bradshaw, in a statement released late yesterday, said RCA "cannot and will not permit Mr. Agee to unilaterally exercise initiatives which may be counterproductive." Under Bradshaw, RCA is attempting a difficult and far-reaching reorganization, selling off some major divisions and channeling its technology and research in new directions. It disclosed to shareholders yesterday that it lost $106.8 million last year and a total of $183.7 million during the past three years in development and sale of its video disc system.

"This is precisely not the time for us to permit anyone to attempt to meddle with, or in any way destabilize, the effort under way right now," Bradshaw said.

A Bendix spokesman, informed of RCA's reaction, said the offer remained a friendly one. "I'm a little surprised," the Bendix spokesman said.

In the past year, Agee has built a $572 million pol of cash and marketable securities by selling off parts of Bendix's diversified businesses, promising to use these funds to establish Bendix in new areas f high technology. Until now, Agee has kept this huge fund i nreserve, earning high rates of interest in short term investments. The purchase of RCA stock was not part of the high technology investment strategy, the Bendix spokesman said.