mechanics year 2

Question 1

vectors in 3D

Answer 1

• draw z axes coming ‘out of the page’ and draw x and y axis as normal, so z-axis points towards the ceiling and is coming out of the page
• axes can be modelled using right hand. Position thumb, forefinger and second finger in the direction of the x, y and z axis respectively
• magnitude of vector r= ai + bj + ck is
  |r|= root (a2+b2+c2)
• the direction of r makes angle alpha with the positive x-axis, beta with the positive y-axis and λ with the positive z axis, where cosalpha= a/ |r|
  cosbeta= b/|r| and cos λ= c/|r|
  it follows that cos2alpha + cos2beta + cos2 λ = (a2 + b2+ c2)/ |r|2 =1