Dry brittle straw like hair is a sign of low thyroid(hypothyroidism and iodine deficiency). Note not all hypothyroidism is caused by iodine deficiency there are multiple causes such as hormonal imbalances, adrean insufficiency, other endocrine problems, nutrient deficiency etc.
Vegan diets can be low in the mineral iodine if your produce isn't growin in adequate soil which to be fair covers alot of our produce these days. Eggs, dairy, cheese are the main dietary sources of iodine and being that vegan's don't include these foods in there diet iodine can be a problematic nutrient for some. Seaweeds are really only reliable plant source of iodine but many can't hack the taste of them which is another problem. I would supplement personally with a little kelp powder if not consuming seaweeds semi-regularly and following a 100% vegan diet.
Omega-3 deficiency can also cause dry hair and skin and vegans sometimes also find omega-3 to be a problematic nutrient to get. Good plant sources of omega-3 include soy/tofu products, nuts, seeds(chia,hemp in particular is very balanced omega-3/6 ideal ratios), flax, some dark leafy greens are a source of good fats. Vegans require the body to convert the fatty acid ALA into EPA and DHA and thus can sometimes have lower levels than meat eaters, there are good vegan DHA supplements which can be beneficial for some.
Amla & Vegan Blog