# What is the components of a unit vector, with an opposite direction to the vectors: A(2,5,6) and B(3,3,4)?

Asked on by juno60

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to find first the opposite vector to `barA`  such that:

`-barA = lt-2,-5,-6gt`

You need to convert the opposite vector in the opposite unit vector, hence, you need to evaluate the magnitude of opposite vector and then, you need to divide the components of opposite unit vector to the magnitude, such that:

`|-barA| = sqrt((-2)^2 + (-5)^2 + (-6)^2)`

`|-barA| = sqrt(4+25+36)`

`|-barA| = sqrt65`

Hence, evaluating the components of opposite unit vector`-barA ` yields `lt-2/sqrt65 ; -5/sqrt65 ; -6/sqrt65gt.`

You need to find first the opposite vector to barB such that:

`-barB lt-3,-3,-4gt`

`|-barB| = sqrt((-3)^2 + (-3)^2 + (-4)^2)`

`|-barB| = sqrt(9+9+16)`

`|-barB| = sqrt34`

Hence, evaluating the components of opposite unit vector -`barB`  yields `lt-3/sqrt34 ; -3/sqrt34 ; -4/sqrt34gt.`

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