Question

For the vectors in the figure, with a = 16, b = 12, and c = 20 what are (a) the magnitude and (b) the direction vector a x vector b (c) magnitude (d) direction vector a x vector c and (e) magnitude and the direction vector b x vector c

Answer 1

please can you make a drawing of your question?

Answer 2

@Michele_Laino here's the drawing for the question :)

Answer 3

we can rewrite your vectors using the component notation, as follows:
\[\begin{gathered}
{\mathbf{a}} = \left( {a,0} \right) \hfill \\
{\mathbf{b}} = \left( {0,b} \right) \hfill \\
{\mathbf{c}} = \left( {a,b} \right) \hfill \\
\end{gathered} \]

Answer 4

where:
a is the magnitude of the vector a, b is the magnitude of the vector b, and c is the magnitude of the vector c

Answer 5

namely:
\[a = \left\| {\mathbf{a}} \right\|,\quad b = \left\| {\mathbf{b}} \right\|,\quad c = \left\| {\mathbf{c}} \right\|\]

Answer 6

now, we can write the vectror product as the subsequent determinant:
\[{\mathbf{a \times b}} = \left\| {\begin{array}{*{20}{c}}
{\widehat {\mathbf{x}}}&{\widehat {\mathbf{y}}}&{\widehat {\mathbf{z}}} \\
a&0&0 \\
0&b&0
\end{array}} \right\| = \widehat {\mathbf{z}}\left( {ab} \right)\]

Answer 7

where:
\[{\mathbf{\hat x}},\;{\mathbf{\hat y}},\;{\mathbf{\hat z}}\]
are the unit vector on the x, y, and z, axis respectively

Answer 8

oh i get it, so axb is 192? how to know if the magnitude is +z or -z or etc.?

Answer 9

i mean the direction

Answer 10

the magnitude is 192, whereas the direction is the direction of the z-axis and upward