# Let e1 and e2 be unit vectors in the OXY-plane which make angles α and β withthe x-axis. Show that e1 = i cos α + jsin α, e2 = i cos β + jsin β and prove thatcos(α − β) = cos α cos β + sin α sin β

Vikas TU
14149 Points
2 years ago
Dear student
e1 and e2 are unit vector , angle in e1 = alpha .
angle in e2 = beta
e1 is unit vector so on drawing a traingle having alpha angle its x component = Cos$\alpha$ i , and y component = Sin$\alpha$ j
Its magnitude = sqrt (Sin^2$\alpha$ + Cos^2$\alpha$) = 1
Hence e1  = i cos α + jsin α
Similarly on drawing angle $\beta$ angle in e2 . and applying same condition .
e2 = i cos β + jsin β
Hope this helps
Good Luck