Determine the vectors are perpendicular

Question

Assignment:

1) Given three vectors; F₁ = 35, F₂ = 40, F_s = 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 -
c) F₁ + F₂
d) F₂F₁
e) F₂ (F₁ + F₂)/F₁

For the vector A= -8j + 4k, find it's 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, P. = 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 = + 2j -5k, F = 2i- 7j + k.