How do you find the unit vector parallel to the resultant of the vectors A= 2i - 6j -3k and B = 4i + 3j- k?

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Answer 1 · 2016-08-11T18:32:27

The Reqd. Unit Vector #=(6/sqrt61,-3/sqrt61,-4/sqrt61)#.

Let a non-null vector #vecx# be given. Then, a unit vector parallel to #vecx# is

denoted by #hatx# and is defined by,

#hatx=vecx/||vecx||#

#vecA=2hati-6hatj-3hatk=(2,-6,-3), &, vecB=(4,3,-1)#.

Hence, the Resultant of #vecA and vecB#, is #vecA+vecB#, & is,

#vecA+vecB=(2,-6,-3)+(4,3,-1)=(2+4,-6+3,-3-1)=(6,-3,-4)#

#:. ||vecA+vecB||=sqrt{6^2+(-3)^2+(-4)^2}=sqrt61#

Hence, the Reqd. Unit Vector #=(vecA+vecB)/||vecA+vecB||#

#=1/sqrt61(6,-3,-4)=(6/sqrt61,-3/sqrt61,-4/sqrt61)#.