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Komok [63]
3 years ago
7

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

Mathematics
1 answer:
lutik1710 [3]3 years ago
5 0

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

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

So, unit vector opposing the \hat{v} is :

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

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

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

Hence, this is the required solution.

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