The plant's deep roots can be attributed to geotropism (or gravitropism), which is the response of a plant to gravity, causing roots to grow downwards. The tendrils wrapping around objects is a response known as thigmotropism, which is the growth movement exhibited by plants in response to touch or physical contact with objects.
Thus, the correct pair of tropisms that describe these responses is:
Geotropism and Thigmotropism.