The vectors OA and OB are such that OA = 4 / 7OB, and the distance between points a and b is equal

The vectors OA and OB are such that OA = 4 / 7OB, and the distance between points a and b is equal to 27. Find the length of the vector OA.

Solution

1. ОА = 4 / 7ОВ, vector length AB = 27

2.we know that the vector AB is equal to the sum of the vectors AO and OB

3. AO is equal to -OA. Ie AO = -4 / 7ОВ, AB = -4 / 7ОВ + ОВ = 3 / 7ОВ

4.27 = 3 / 7ОВ, ОВ = 27: (3/7) = 27 × (7/3) = 9 × 7 = 63

5.the length of the vector AB is equal to the sum of the lengths of the vectors OA and OB

6.AO = AB – OB, AO = 27 – 63, AO = -36

7. | OA | = | AO |, | OA | = | -36 | = 36

The answer is the length of the vector OA is 36