Vector addition

The second question in Sadlers 3C Specialist textbook requires the addition and multiplication of 3 dimensional vectors.

Addition of vectors

When showing the addition of vectors, we place them end to end. The resulting vector (from the start of the first vector to the end of the last can then be determined.

The initial process outlined for showing a vector required that it always start from the origin. When adding vectors, the second vector needs to start from the end of the first. Therefore, rather than using the command HOME we can reverse the vector directions

TO VECTOR :X :Y :Z
PU
EAST :X UP :Y SOUTH:Z
MAKE “A POS
EAST -:X UP -:Y SOUTH -:Z
LINE
PD
SETPOS “A
END

The second issue we face is the need for 2 vectors, hence we need to define 2 vector – VECTORA and VECTORB, in the second, MAKE “A POS becomes MAKE “B POS and MAKE “A becomes MAKE “B

If we now use the command

VECTORA :X :Y :Z
VECTORB :X :Y :Z

We can see our 2 vectors placed end to end.

• To determine the resultant vector we use

;
LABEL POS

• If we need to show the resultant vector,

PU HOME
PD SETPOS “B

• Note – more vectors can be added as needed.

Example

CS
AXIS
VECTORA 1 3 2
VECTORB 2 1 -4
LABEL POS
PU HOME
PD SETPOS :B