Question

Two friends while flying kites from different locations, find the strings of their kites crossing each other. The strings can be represented by vectors `veca = 3hati + hatj + 2hat k and vecb = 2hati - 2hatj + 4hatk`. Determine the angle formed between the kite strings. Assume there is no slack in the strings

Answer 1

Given: `veca = 3hati + hatj + 2hat k`

`vecb = 2hati - 2hatj + 4hatk`

We know that,

cos θ = `(veca ⋅ vecb)/(|veca||vecb|)`

cos θ = `((3hati + hatj + 2hat k) ⋅ (2hati - 2hatj + 4hatk))/(|3hati + hatj + 2hat k||2hati - 2hatj + 4hatk|)`

cos θ = `(6 - 2 + 8)/(sqrt(9 + 1 + 4)  sqrt(4 + 4 + 16))`

cos θ = `(12)/(sqrt14  sqrt24)`

cos θ = `(12)/(sqrt14 xx 2sqrt6)`

cos θ = `sqrt(6/14)`

cos θ = `sqrt(3/7)`

θ = `cos^(-1)sqrt(3/7)`