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प्रश्न
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
बेरीज
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उत्तर
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)`
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