Question

if Avector=2i+3j+4k and Bvector=3i-5j+k find the angle between A and B if both are parallel​

Answer 1

Answer:

Given,

a⃗ =(2,3,4)

b⃗ =(3,4,5)

Therefore,

∥a⃗ ∥=22+32+42−−−−−−−−−−√=29−−√

∥b⃗ ∥=32+42+52−−−−−−−−−−√=50−−√

a⃗ ⋅b⃗ =6+12+20=38

From the dot product definition, we have:

cosθ=a⃗ ⋅b⃗ ∥a⃗ ∥∥b⃗ ∥

Where θ is the angle between the two vectors a⃗ and b⃗ .

Therefore,

cosθ=3829√×50√

θ=arccos(3829√×50√)

θ=3.688∘