Q1.4 Adding vectors (K)
Consider two vectors





- What is the direction of
? Draw a vector diagram showing the relationship between the three vectors. Deduce the magnitude of the vector
.
- On your vector diagram add rectangular x and y coordinate axes
representing east and north directions respectively. Mark unit vectors î
and
on these axes. Read off the values of the components Ax ,Ay ,Bx , By. Deduce the magnitude and direction of
this way.
- What is C ? What is A+B ? Comment.
Hint
Reveal

Hint
It is often possible to determine the direction of a vector by inspection.
In this case you should immediately be able to ‘see’ what the direction of
is.
The point of the last part is to get you to distinguish between adding vectors and adding the magnitudes of those vectors.
Solution
Reveal

Solution
- Once you have drawn
and
, or even pictured them in your mind’s eye, you see immediately that
must be vertically upwards (or north).
It is obvious isnt it? A physicist might well put a gloss on this by citing the ‘symmetry’ of the two vectors
and
.
Once you’ve decided this it is easy to see how the vector triangle fits together; to see that it is a right-angled triangle; and to deduce (Pythagoras) that
- Constructing the axes and unit vectors as asked we identify:
andIt follows thatwhich expresses both the magnitude and the direction of
.
Finally while
The point here is to emphasize the difference between vector and scalar addition. In my experience many students take a long time to learn this. If you are uncertain save yourself some pain by sorting it out now. Your tutor is there to help!