Question

Given that vector p+q+r=0./p/=3, /r/=5, /q/=4 what's the angle between vector p and r

Answer 1

Angle between P and q is ∅

now,

P + q = -r

take magnitude

p² + q² +2p.qcos∅ = r²

P² +P² +2p.qcos∅= 2P²

cos∅ = 0

∅ =π/2

angle between q and r ∅'

q + r = -P

take magnitude

q² + r² +2rpcos∅'=p²

p² + 2p² +2.√2P.P cos∅' =P²

cos∅' =-1/√2

∅ = 3π/4

angle between r and P is ∅"

P + r = -q

take magnitude

P²+ 2P² +2√2p²cos∅" = P²

cos∅" =-1/√2

∅" = 3π/4

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