Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = i + 29j, b = 15i + j

Two vectors a and b are given. Determine the dot products a ⋅ b and a ⋅ a:

a = -17i - 9j, b = -8i - 12j

Find a ⋅ b + a ⋅ c using the following vectors:

a = 9i - 4j, b = i + 5j, c = 8i + 3j

For the vectors, a and b, determine the angle between both vectors. 

a = 6cos(7π/3)i +6sin(7π/3)j, b = 12cos(5π/2)i +12sin(5π/2)j

Assess whether a and b are parallel, orthogonal, or do not possess either property. 

a = 6i +11j, b = 5i -(30/11)j

For the given vectors a and b, compute the scalar product followed by determining the angle between the two vectors. Round the angle to the nearest tenth of a degree. 

a = 3i +17j, b = 21i -2j