How do you normalize (- 2i - j - k)(−2i−j−k)?

1 Answer
Nathan L.
Aug 14, 2017

hatv = -sqrt(2/3)hati - 1/(sqrt6)hatj - 1/(sqrt6)hatkˆv=−√23ˆi−1√6ˆj−1√6ˆk

Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of the vector in question.

The equation for the normalization of a vector (which I'll call vecv→v) is given by

(vecv)/(||vecv||)→v∣∣∣∣→v∣∣∣∣

where ||vecv||∣∣∣∣→v∣∣∣∣ is the magnitude of vector vecv→v.

The magnitude of vecv→v is

||vecv|| = sqrt((-2)^2 + (-1)^2 + (-1)^2) = color(red)(ul(sqrt6

Thus, the unit vector (hatv) will be

hatv = (-2)/(color(red)(sqrt6))hati - 1/(color(red)(sqrt6))hatj - 1/(color(red)(sqrt6))hatk

color(blue)(ulbar(|stackrel(" ")(" "hatv = -sqrt(2/3)hati - 1/(sqrt6)hatj - 1/(sqrt6)hatk" ")|)

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