For me, diagrams make it much easier to make sense of what is going on - I can represent a position vector as a point on the diagram with a line segment coming from the origin.
Direction vectors just become line segments joined onto other vectors, with a helpful arrow to remind me that $\mathbf$ and $\mathbf$ are in opposite directions!
Start by solving vector problems in two dimensions - it's easier to draw the diagrams - and then move on to three dimensions.
(For four or more dimensions, it becomes more difficult to visualise!
A final word on notation; in type, vectors are indicated by bold type.
In handwriting, it is a convention to underline vectors and leave scalars (such as the constants $k$ and $\lambda$ above without underlining.
Many students are often reluctant to tackle questions using vectors.
I think this is partly because often vectors is not taught until quite a way through a school maths course, so they are unfamiliar.
Consider the point on the tire that was originally touching the ground.
How far has it displaced from its starting position? (moderate) A student carries a lump of clay from the first floor (ground level) door of a skyscraper (on Grant Street) to the elevator, 24 m away. Finally, she exits the elevator and carries the clay 12 m back toward Grant Street.