by The Open University
Available in 11 free installments
Owner:
The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.
Find the magnitude and direction of the sum of the two vectors which were specified in Activity 1 giving your answers correct to two decimal places. (You will need to choose different labels for the two vectors.)
Adopting the labels p and q for the two given vectors, you found in Activity 1(a) that the component forms were (to 4 d.p.)
Their sum is
The magnitude of the vector r = p + q is
Since the components of r are r 1 = 1.3231, r 2 = 1.9640, we have
Also, (1.3231, 1.9640) lies in the first quadrant, so the direction of r is θ = φ ≈ 56.03°.
Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence
