CASE STUDY CHALLENGE

Vector Algebra: Movement Plan

Three friends A, B, and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B, after reaching their destinations, will meet up with C at his decided destination.

Vector Movement Diagram

They follow straight paths from A to C and B to C. Their position vectors are given as:

  • • OA = a
  • • OB = b
  • • OC = 5a – 2b

Answer the following:

(i) Complete the movement plan by describing the vectors along the paths from A to C and B to C. [1]
(ii) Find the vectors AC and BC in terms of a and b. [1]
(iii)

(a) If a · b = 1, distance |OA| = 1 km, and |OB| = 2 km, find the angle between OA and OB. Also find |a × b|.

— OR —

(b) If a = 2î – ĵ + 4k̂ and b = ĵ – k̂, then find a unit vector perpendicular to both (a + b) and (a – b).

 [2]
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