Homework $1$

AERO $211-200,-500$: Aerospace Engineering Mechanics

Topics Covered: Coordinate systems, Vectors, Componentiation.

Note: Anything written in boldface is a vector.

Problem $1$

Using the vectors shown in the Fig. $1,$ answer the following questions:

Figure $1$: Vectors an un pavunan vi aneseas

a$.$ Express $a$ in terms of the basis vectors $I\{hat(i{)}_1,$hat$(i{)}_2,$hat$(i{)}_3\},$ that is to say, fill in the blanks in the equation:

b$.$ What is the magnitude of $a?$

c$.$ Express $b$ in terms of hat$(i{)}_3$ and $a.$ Hint: Note the plane in which a lies.

d$.$ Using the results above, finally, write $b$ in terms of the basis vectors $I\{hat(i{)}_1,$hat$(i{)}_2,$hat$(i{)}_3\},$ that is to say, fill in

the blanks in the equation given below:

e$.$ What is the magnitude of $b?$

f$.$ Evaluate the cross product $(bx{}_3^{}),$ express the answer in terms of the $I\{hat(i{)}_1,$hat$(i{)}_2,$hat$(i{)}_3\}$ vectors.