Question

V= -3i-4sqrt2, find a unit vector that points in the opposite direction as v

Answer 1

The unit vector in the opposite direction of u is:

`\vec{u} =-(1)/(√(23))<-3i-4,√(2)>`

Explanation:

To find the unit vector suppose u that points in the opposite direction as v

`\vec{v}=<-3i,-4√(2)>`

we use the formula:

`\vec{u} =-\frac{1}{||\vec{v}||}\vec{v}`

Finding
`||\vec{v}||`

`||\vec{v}|| = √(x^2+y^2)\\||\vec{v}|| = \sqrt{(3i)^2+(4√(2)^2} \\||\vec{v}|| = √(9i^2+(16*2))\\ i^2 = -1\\||\vec{v}|| = √(9(-1)+32)\\||\vec{v}|| = √(-9+32)\\||\vec{v}|| = √(23)`

`\vec{u} =-(1)/(√(23))<-3i,-4√(2)>`

The unit vector in the opposite direction of u is:

`\vec{u} =-(1)/(√(23))<-3i,-4√(2)>`