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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

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

Grade:12

1 Answers

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 

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