Vector Direction uestion?

Question

a = 5 i − 2 j + 4 k

How would i go about finding a unit vector having the same direction as a and finding a unit vector oppositely directed to a?
Working out would be great.
Thanks

Answer 1

the size of this vector is sqrt(5**2+2**2+4**2)=6.7

So: unit vector = 5/6.7 i -2/6.7j + 4/6.7k

to get the opposite directions change all + to - , and all - to +

Answer 2

to get the unit vector divide a by magnitude of a

unit vector of a = a/|a|

... in the opposite direction: -a/|a|


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Answer 3

find the magnitude of a then divide a by the magnitude of a