Question 1206235
Vector A lies in the y-z plane 63° from the positive y-axis and has a magnitude 3.2. 
<pre>
It's in the y-z plane, means its x-component is 0.
Its y-component is 3.2cos(63<sup>o</sup>) 
Its z-component is 3.2sin(63<sup>o</sup>) 

Its components are < 0, 3.2cos(63<sup>o</sup>), 3.2sin(63<sup>o</sup>) >
or in i,j,k form

0i + 3.2cos(63<sup>o</sup>)j + 3.2sin(63<sup>o</sup>k 

or just 3.2cos(63<sup>o</sup>)j + 3.2sin(63<sup>o</sup>k
as in this form it is unnecessary to write a 0 component.</pre>
Vector B lies in the x-z plane 48° from the x-axis and has a magnitude 1.4.
Find A.B, AxB and the angle between A and B<pre>

It's in the x-z plane, means its y-component is 0.
Its x-component is 1.4cos(48<sup>o</sup>) = 0.9367828489
Its z-component is 1.4sin(48<sup>o</sup>) = 1.040402756

Its components are < 0, 1.4cos(48<sup>o</sup>), 1.4sin(48<sup>o</sup>) >
1.4cos(48<sup>o</sup>)i + 0j + 1.4sin(48<sup>o</sup>)k 

or just 1.4cos(48<sup>o</sup>)i + 1.4sin(48<sup>o</sup>)k
as in this form it is unnecessary to write a 0 component.

To find {{{A*B}}}, the dot product, which is the scalar product, is
a plain old number, not a vector!

{{{A*B}}}{{{""=""}}}{{{matrix(1,5,""< 0,",", 3.2cos(63^o),",", 3.2sin(63^o) >"")}}}{{{""*""}}}{{{matrix(1,5,""<1.4cos(48^o), ",",0,",", 1.4cos(48^o)>"")}}}{{{""=""}}}
{{{matrix(1,5,(0^""^"")(1.4cos(48^o)^""),""+"", (3.2cos(63^o)^"")(0^""^"")       ,""+"", (3.2sin(63^o)^"")(1.4cos(48^o)^""))}}}{{{""=""}}}
{{{(3.2sin(63^o)^"")(1.4cos(48^o)^"")}}}


To find A x B. Work out this determinant, which will come out 
in i,j,k form. This is the cross-product, or the vector-product. Unlike
the dot product, which is plain old number, the vector-product is a vector.

{{{AxB}}}{{{""=""}}}{{{abs(matrix(3,3,i,j,k,
  0, 3.2cos(63^o), 3.2sin(63^o),
1.4cos(48^o),0, 1.4sin(48^o)))}}}

Edwin</pre>