Question

What is the angle between `<6,9,1>` and `<5,6,7>`?

Answer 1

`alpha=37^o`

Explanation:

`vec A= <6,9,1> " "vec B= <5,6,7>`
`1-"find magnitude of the vector " vec A and vec B`
`||A||=sqrt(6^2+9^2+1^2)" "||A||=sqrt(36+81+1)=sqrt118`
`||B||=sqrt(5^2+6^2+7^2)" "||B||=sqrt(25+36+49)=sqrt110`
`2-"find dot product of A and B"`
`A.B=6*5+9*6+1*7=30+54+7=91`
`3-"use the formula of dot product"`
`A.B=||A||*||B||*cos alpha`
`91=sqrt 118*sqrt 110*cos alpha`
`cos alpha=91/sqrt(118*110)`
`cos alpha =91/(113,93)`
`cos alpha=0,798736066005`
`alpha=37^o`