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.

RI
Answered by Rafiqul I. Maths tutor

19508 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

f(x) = x^3+2x^2-x-2 . Solve for f(x) = 0


For y = 7x - x^3, find the two stationary points and what type of stationary points they are.


A medical test will be positive for 0.05% of people and negative for everyone else. Suppose a hospital will test 4000 patients each day. Use an appropriate approximation to find the probability that 5 people test positive tomorrow. (5SF)


Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning