Vectors Questions with Step-by-Step Solutions

Choose axes first, then resolve every vector consistently. Components add algebraically; magnitudes do not. For an angle measured from the positive x-axis, cosine usually gives the x-component and sine gives the y-component, but a different reference angle can swap those roles.

Sketch the resultant before calculating so its signs and quadrant are predictable. When converting components back to a direction, use an atan2-style quadrant check instead of trusting a bare inverse tangent value.

Write each vector as an ordered component pair, add the pairs, and convert the result to magnitude and direction only at the end. Use the worked problems to compare coordinate choices and practice one example with a vector in a different quadrant.