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 = 11i - 3j, b = -10i - 8j

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

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

Are the vectors a and b orthogonal?

a = 12i - 6j, b = 5i + 10j

Determine the projection of vector a onto vector b. Next, express vector a as vectors, a₁ and a₂, where a₁ is parallel to vector b and a₂ is perpendicular to vector b. 

a = 11i -j, b = 3i +9j

Find the angle between the two vectors. Express the angle in degrees and round it to two decimal places.

$〈15, 0〉, 〈5, 3〉$