Question

9.1 Resolve the force vector F = (990 N)i - (330 N) j + (660 N)k into two components, one parallel to vector a = i + 3k , the other perpendicular to a .

Answer 1

let (990i -330j + 600k) = s( ui + vj + wk) + t ( i + 3k) , where s and t is the parameter and ( ui + vj + wk) dot ( i + 3k) = 0

now you have 4 equations, solve for u and v in terms of w them factorise them out. Find the parameter, t in terms of s and w

Answer 2

you'll get (990 i -330 j + 660k) = -33( -21i + 10j +7k ) + 297 ( i + 3k)

Answer 3

where -33 ( -21 i +10 j +7k ) is your perpendicular vector and 297(a) is the parallel vector.