5 The vectors uv are given by u 3i5 are given by u 3vi2 Fin

5. The vectors u,v are given by u 3i+5/ , are given by u -3+%,vi-2. Find scalars a, b such that aluv) 8i+ (b-2/. Working Answer: Total 4 marks)

u = 3i+5j
v = i-2j

a(u+v) = 8i+(b-2)j

a(3i+5j+i-2j) = a(4i+3j) = 8i+(b-2)j

Comparing 1 and 2 we have:

4ai = 8i, 4a=8, a=2
3aj = (b-2)j, a=2 therefore, 6j = (b-2)j, b = 8

a = 2, b = 8