Use the definition of scalar product, a overscript right-arrow endscripts times b overscript right-arrow endscripts = ab cos θ, and the fact that a overscript right-arrow endscripts times b overscript right-arrow endscripts = axbx + ayby + azbz to calculate the angle between the two vectors given by a overscript right-arrow endscripts equals 3.0 i overscript ̂ endscripts plus 3.0 j overscript ̂ endscripts plus 3.0 k overscript ̂ endscripts and b overscript right-arrow endscripts equals 5.0 i overscript ̂ endscripts plus 7.0 j overscript ̂ endscripts plus 6.0 k overscript ̂ endscripts.

The following vectors have been given:

The angle between these two vectors can be found by:

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day