% MotionGenesis file: MGVectorExample.txt
%---------------------------------------------------
% Create sets of right-handed orthogonal unit vectors.
RigidFrame A   % Creates Ax>, Ay>, Az>
RigidBody  B   % Creates Bx>, By>, Bz>

%---------------------------------------------------
% Define other vectors in terms of these unit vectors.
v> = 2*Ax> + 3*Ay> + 4*Az>
w> = Vector( A, 6, 7, 8 )
F> = Vector( B, [3, 5, 7] )

% Multiply the vector v> by 5.
vFive> = 5 * v>

% Add vectors v> and w>.
addVW> = v> + w>

% Dot-multiply  v>  with  w>.
dotVW = Dot( v>, w> )

% Cross-multiply  v>  with  w>  and form  w> x (w> x v>).
crossVW> = Cross( w>, v> )
crossWWV> = Cross( w>, Cross(w>,v>) )

% Find the magnitude and magnitude-squared of v>.
magV = GetMagnitude( v> )
magVSquared = GetMagnitudeSquared( v> )

% Form the unit vector in the direction of v>.
unitV> = GetUnitVector( v> )

% Find the radian-measure of the angle between v> and w>.
angleBetweenVW = GetAngleBetweenVectors( v>, w> )

% Form the ordinary time-derivative of the vector  t*v> + sin(t)*w>  in reference frame A.
vectorDerivative> = Dt( t*v> + sin(t)*w>, A  )

% Form a rotation matrix relating  Bx>, By>, Bz>  to  Ax>, Ay>, Az>  in terms of time t.
B.SetRotationMatrixZ( A, t )

% Express vector v> in terms of Bx>, By>, Bz>.
Express( v>, B )

% To express vector  v> + F>  in terms of  Ax>, Ay>, Az>,  type
sumInTermsOfAxyz> = Express( v> + F>,  A )

% Form the  Bx>, By>, Bz>  measures of w>.
wMatrix = Vector( B, w> )

% Save input and output responses.
Save MGVectorExample.html

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