Given these two vectors [1,2,3] and [4,5,6] how would look for their unit vectors?

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember what is the formula that allows you to evaluate the unit vector such that:

`bar u = (bar v)/(|v|)`

Reasoning by analogy, you may find the unit vectors `bar (u_1)` and `bar(u_2)` such that:

`bar (u_1) = (bar v_1)/(|v_1|)`

`bar (u_1) = (<1,2,3>)/(sqrt(1^2+2^2+3^2))`

`bar (u_1) = (<1,2,3>)/(sqrt(1+4+9))`

`bar (u_1) = (<1,2,3>)/(sqrt14) => bar (u_1) = <1/sqrt14,2/sqrt14,3/sqrt14>`

`bar (u_2) = (bar v_2)/(|v_2|)`

`bar (u_2) = (<4,5,6>)/(sqrt(4^2+5^2+6^2))`

`bar (u_2) = (<4,5,6>)/(sqrt(16+25+36))`

`bar (u_2) = (<4,5,6>)/(sqrt77) => bar (u_2) = <4/sqrt77,5/sqrt77,6/sqrt77>`

Hence, evaluating the unit vectors of the given vectors `v_1` and `v_2` yields `bar (u_1) = <1/sqrt14,2/sqrt14,3/sqrt14> ` and` bar (u_2) = <4/sqrt77,5/sqrt77,6/sqrt77>` .