How do you find a vector of length 1 in the same direction as (6,-8)?

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Answer 1 · 2016-08-29T13:29:44

The reqd. vector is #(6/10,-8/10)#.

The Reqd. Vector, say #vecx# is in the same direction as #(6,-8)#, we must have,

#vecx=k(6,-8)=(6k,-8k),# where, #k in RR^+#.

As the second requirement for #vecx# is #||vecx||=1#, we have,

#36k^2+64k^2=1#, i.e., #100k^2=1#, or, #k=+-1/10#, but, as, #k>0#,

#k=+1/10#.

Therefore, the reqd. vector is #(6/10,-8/10)#.

Enjoy Maths.!