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

Question

asked Jul 21, 2022 212k views

1 Answer

Dpetrini · Answer 1 · 2022-07-25T03:26:29+0000

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

$\hat{v} = (3i + j -4k)/(√(3^2 + 1^2 + 4^2))\\\\\hat{v} = (3i + j -4k)/(5.1)$

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

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

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

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

Hence, this is the required solution.