Physics · Vectors and equilibrium. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A vector has magnitude and direction. In Cartesian coordinates it is written with the unit vectors i, j and k along the x, y and z axes, for example A = Axi + Ayj.
Any vector can be replaced by two perpendicular parts called its rectangular components. If the vector makes an angle θ with the positive x-axis, the x-component uses cos θ and the y-component uses sin θ.
To add vectors, draw them head to tail; the resultant goes from the tail of the first to the head of the last. By calculation, add all the x-components, add all the y-components, then combine the two totals with Pythagoras' theorem.
Students give the calculator value of tan−1 as the direction without checking the quadrant. Look at the signs of both components first, then use the quadrant rule.
Answer: 26.5 units at 40.9° to the positive x-axis
Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.
← Dimensions of physical quantitiesProduct of two vectors →Take a Physics test