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Find a vector 3 units long in the opposite direction from v = 〈3, 1,-4).

Sagot :

Unit vector along the direction v = <3,1,-4> is :

[tex]\hat{v} = \dfrac{3i + j -4k}{\sqrt{3^2 + 1^2 + 4^2}}\\\\\hat{v} = \dfrac{3i + j -4k}{5.1}[/tex]

So, unit vector opposing the [tex]\hat{v}[/tex] is :

[tex]\hat{v'} = -\hat{v}\\\\\hat{v'} = -( \dfrac{3i + j -4k}{5.1})\\\\\hat{v'} = \dfrac{-3i - j +4k}{5.1}[/tex]

so, vector of magnitude 3 units in opposite direction from v is :

[tex]\vec{V} = 3\hat{v'}\\\\\vec{V} = \dfrac{3}{5.1}( -3i -j+4k)[/tex]

Hence, this is the required solution.

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