Ketu in 3rd house in Astrology is not good as it ruins the relationship with siblings or restricts the contact with them, it gives bad marriage or delay in marriage, and makes the person do bad deeds.
The 3rd House indicates Short distance travel, like state to state, or from one town to another like a truck driver. The third house also represents siblings and relationships with them, media, networking skills, writing, and speaking ability. This house also promotes courage. It's the house of willpower and your efforts. Where your efforts will be and how much effort will you put in your work. This is also the house of longevity since it's 8th from the 8th house.
The third house represents the interaction with siblings and is an important part of the early life experience (before school years). It is a great exploration and discovery journey, learning how to communicate and build up strength and independence. Physically, the next parts of the body are the shoulders and arms. The significance of arms and hands also brings in manual dexterity. The correspondence with Mithuna (Gemini) adds communication.
Ketu is the south node of the Moon and the rest of the body of Rahu. This is a headless body representing separation, isolation, and the abandonment of the material world. This shadow planet represents spirituality, nothingness, and goals that we already achieved in past lives. In this life, we only rely on those things as a last resort.
Ketu in Vedic Astrology is also an unsteady and sometimes treacherous force. Still, its qualities are more of an abstract, inward nature, in contrast to Rahu, who is more concerned with outward, worldly matters. Ketu can bring hindrance and obstacles in the physical realm of life but indicates sparks of intelligence and brilliance of the mind. The above significations are extremely important to know by heart. You should memorize them and use them often to remind yourself of the essential nature of the Grahas.
Note: The degree of auspiciousness and inauspiciousness will depend upon a complete analysis of the horoscope (birth-chart).