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

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Vikas TU · Answer

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 i , and y component = Sin j Its magnitude = sqrt (Sin^2 + Cos^2 ) = 1 Hence e1 = i cos α + jsin α Similarly on drawing angle angle in e2 . and applying same condition . e2 = i cos β + jsin β Hope this helps Good Luck

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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

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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

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