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 $=(vecA+vecB)/||vecA+vecB||$

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