F = 5i + 3j. Find the magnitude and direction of F?
i is the unit vector (magnitude of 1) in the direction of the positive x-axis. j is the unit vector in the direction of the positive y-axis. The magnitude of F would be the length of the hypotenuse of a right-angled triangle with a base of 5 and a height of 3. Using Pythagoras’ theorem,│F│ = √(52 + 32) = √34 = 5.83 (to 3 s.f.)The direction of a vector is measured anti-clockwise from the positive x-axis (unless a required direction is specified in the question, e.g. angle from the positive y-axis). By drawing the triangle, you can use trigonometry to find the angle. In this case,θ = tan-1(3/5) = 31.0°Remember underlining vector notation on paper is important as this shows it is bold and hence a vector.
