Practice Questions
Clement Radcliffe, Contributor

I will continue the review of VECTORS, with the solution to the homework. Given the following diagram which shows vectors b and c.

Express in the form

(i) b
(ii) c

SOLUTION

(iii) Please look at the diagram for the position of vectors x and y. Do you agree with the plot of these vectors? If not, please review the materials given previously.

Continuing the review of VECTORS.

The arithmetic operations may be applied to vectors as follows.

I do hope that you realize that the negative sign reverses the direction of the vector.

Let us attempt the following examples which will clearly illustrate the above. It is advisable that you evaluate the answers and check them against mine.

In number (3) above could you use the Cartesian diagram to investigate the relationship between the vectors b and 2b.

NB: Did you notice the 2b is twice the length of b and in the same direction? If you have mastered the above we will go on to a Special Vector - THE POSITION VECTOR.

POINTS TO NOTE

• The position vector always begins at the origin.
• It is denoted by p or alternatively where O is the origin.
• Given the point P (2,3) then the position vector =

While the aspects of vectors presented above are relatively simple the points noted are sometimes missed by student to their detriment. Please note them well.

HOMEWORK

In the diagram above, A and B are points such that = a and = b. The point P (not shown) is such that = 1/2 a + b,

(i) Write in the form

(ii) Determine the length of OP.

Please remember that the exams are a few weeks away. You need to reflect this in your revision.

The Cartesian diagram below illustrates why the coordinates of P x1, y1) are the same as the components of the Position Vector =

From the Cartesian diagram did you notice that unlike the Position Vector , the coordinates of A (-3, 1) and B (-1, 4) are different from the components of the vector = ?

LENGTH OF VECTOR ON CARTESIAN DIAGRAM

As = may be illustrated as
Then AB² = 2² + 3² using Pythagoras Theorem ie. AB² = 4 + 9 ie. AB = It follows that for vector = , then the length of AB² = x² + y²

Clement Radcliffe is the principal of Glenmuir High School in May Pen.