1) Given three vectors; F1 = 35, F2 = 40, F3 = 80 (see the diagram for the angles), find the resultant vector of all three using the component method.
2) Repeat Problem #1 using unit vectors. Make sure you write out each vector using unit vectors first and show ALL of your work.
3) Using the vectors F1 and F2 from Problem #1, find the following, leaving your answers in unit vector notation.
a) F1 - F2
b) 2F2 - F1
c) F1 + F2
d) F2F1
e) F2 (F1 + F2)/ F1
4) For the vector A = - 8j + 4k, find its magnitude and direction. Also state in what plane the vector resides.
5) Given the vector: A = 3i + 4j, find any three vectors B that also lie in the xy plane and have the property that A = B but A ≠ B. Write out these vectors with unit vector notation.
6) Given two vectors; S = 2.5, R = 4.2, (see the diagram for the angles), find the dot product using (a) the magnitudes and (b) unit vector notation.
7) Calculate the angle between the two vectors given by:
b = 3i - 2j - 8k, c = i - 5j + 4k.
8) Determine if the following vectors are perpendicular to each other.
a) P = 3i - 2j + k, Q = 4i + 9j + 6k.
b) D = i + 2j - 5k, F = 2i - 7j + k.
9) Determine the vector product of each set of vectors.
a) P = 3i - 2j + k, Q = 4i + 9j + 6k.
b) D= i + 2j - 5k, F = 2i - 7j + k.