Question

find sin theta if theta is the angle between the two i-2j+3k and 3i-2j+k
option : a) 2root6/5
b) 2root6/9
c) 2root6/7
d) 2root6/11​

Answer 1

Answer:

Let the vectors be a⃗ and b⃗ ,

a⃗ =(1,−2,3)

b⃗ =(3,−2,1)

Therefore,

∥a⃗ ∥=1+(−2)2+32−−−−−−−−−−−−√=14−−√

∥b⃗ ∥=32+(−2)2+1−−−−−−−−−−−−√=14−−√

a⃗ ⋅b⃗ =3+4+3=10

From the dot product definition, we know that:

cosθ=a⃗ ⋅b⃗ ∥a⃗ ∥∥b⃗ ∥

Where θ is the angle between the two vectors.

cosθ=1014

θ=arccos1014

θ=44.4153∘

Now,

sinθ=0.6998

Step-by-step explanation:

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