Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1. ? w = i − 5j

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Answer 1 · 2018-04-12T17:26:47

# 1/sqrt26i-5/sqrt26j#.

Let us denote by #hatx#, a unit vector in the direction of a given

non-null vector #vecx#.

We know that, #hatx=vecx/||vecx||#.

#:. hatw=vecw/||vecw||=(i-5j)/sqrt{1^2+(-5)^2}#,

# rArr hatw=1/sqrt26i-5/sqrt26j#.

Verification : #||hatw||=1#.

#||hatw||=sqrt{(1/sqrt26)^2+(-5/sqrt26)^2}=1/26+25/26=1#,