Question

vector A=2i+4j-5k and vector B=i-4j+9k then find the angle between them​

Answer 1

Vector a=2i+3j+4k, and vector b=3i+4j+5k. What is the angle between them?

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∘