Question

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

Answer 1

Answer:

The unit vector in the opposite direction of u is:

$\vec{u} =-\frac{1}{\sqrt{23}}<-3i-4,\sqrt{2}>$

Step-by-step explanation:

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

$\vec{v}=<-3i,-4\sqrt{2}>$

we use the formula:

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

Finding $||\vec{v}||$

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

$\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>$

The unit vector in the opposite direction of u is:

$\vec{u} =-\frac{1}{\sqrt{23}}<-3i,-4\sqrt{2}>$