The resultant of any two vectors can be found by drawing them ‘tip to tail’.The resultant is the vector starting at the ‘tail’ of the first vector and ending at the ‘tip’ of the second, as illustrated.
At Leaving Cert. level we are only required to add vectors that are at right angles to each other.
Triangle Law for perpendicular vectors
Fig 2.7: Illustration of addition of vectors
The resultant of two perpendicular vectors is equal to the hypotenuse of the right-angled triangle formed by the two vectors placed ‘tip to tail’.The second vector starts at the end of the first vector, as illustrated in Fig 2.8.
Fig 2.8: Illustration of addition of perpendicular vectors
Use Pythagoras’ Theorem to get the magnitude of the resultant vector:
Resultant 2Opposite2 Adjacent2 Use SOHCAHTOA to get the direction of the resultant vector: u = tan-1a
Opposite Adjacent b
SAMPLE PROBLEM 2B 12 N 5 N Fig 2.9: Object acted on by 12 N east and 5 N south
Two forces are applied to a body, as illustrated in Fig 2.9, with the 12 N acting in an easterly direction. Calculate the resultant force acting on the body.
SAMPLE ANSWER 2B Fig 2.10: The resultant of the forces 12 N east and 5 N south is shown in red
12 N R 5 N Using Pythagoras’ Theorem and SOHCAHTOA: R2 52 122QR 225 144 13
