Vectors homework

AT THE outset, let us review the homework given last week. 1.The diagram below shows vector b and vector c.

LENGTH OF VECTOR ON CARTESIAN DIAGRAM

The vector AB = 8 may be illustrated on the6Cartesian diagram: As ACB is a right-angled triangle, then using Pythagoras’ Theorem AB2 = AB2 + CB2 AB2 = 82 + 62 = 64 + 36 AB = √100 = 10 It follows that for AB = x, then the length of AB2 = x2 + y2 y While the aspects of vectors presented above are relatively simple, the points noted are sometimes missed by students, to their detriment. Please review and note them well. (ii) Using the formula for length-: OP2 = x2 + y2 [Using Pythagoras’ Theorem] = 82 + 152 = 64 + 225 = 289 length of OP = √289 = 17 I expect that you had no difficulty in understanding the above. If this is the case, let us attempt another example.

EXAMPLE

(a) Using the graph (b) (i) Express each of the position vectors OA and OB in the form x y (ii) Determine the vectors: (a) 3 OA , (b) - 2OB (c) AB hence determine (d) 3OA - 2OB (iii) If OA + OB = | c | , show that c = √34 (i) The coordinates of A and B, respectively, are (3, 4) and (2, -1). The position vectors are OA = 3 and OB 2

4 -1 Note that the coordinates of A and B were used to determine the position vectors OA and OB. You could also have read off the components directly from the graph. In this case, joining OA and OB should make it easier. Answer is 5 14 The ‘hence’ in the question indicates that the answers in (a) and (b) should be used to solve the part (c). While other methods may be used, the method you are directed to use is usually the simplest approach. Always obey the instructions. A common error is to subtract the two vectors found above, instead of adding. This is justified as follows: 3OA - 2OB = 3OA + ( - 2OB) Since you were requested to find vectors ( 3OA) and (- 2OB), you, therefore, add both answers.

HOMEWORK

I wish you a productive week as you continue to review vectors. Next week we will begin the review of matrices.