Vectors: magnitude, direction and products

Use $\mathbf a=(-3,4,0)$ and the unit directions $(1,0,0)$ and $(-1,0,0)$. Sketch the same arrow and its perpendicular foot on the x-axis for both choices. Predict the signs of the scalar components and compare the two projection lengths, parallel vector components and perpendicular lengths. Verify with dot and cross products, explaining why a changed sign need not mean a changed geometric projection.