Find a unit vector in the opposite direction of u. u = $( - 14 , - 3,14 )$
A) $\frac { \sqrt { 31 } } { \sqrt { 401 } } ( - 14 , - 3,14 )$
B) $\sqrt { 401 } ( 14,3 , - 14 )$
C) $( - 14 , - 3,14 )$
D) $\frac { 1 } { \sqrt { 401 } } ( 14,3 , - 14 )$
E) $\frac { 1 } { \sqrt { 31 } } ( - 14 , - 3,14 )$

Question

Quizplus · Accepted Answer

To find a unit vector in the opposite direction of $u = (-14, -3, 14)$, first calculate the magnitude of $u$, which is $\sqrt{(-14)^2 + (-3)^2 + 14^2} = \sqrt{196 + 9 + 196} = \sqrt{401}$. A unit vector in the opposite direction is obtained by dividing each component of $u$ by its magnitude and changing the sign, resulting in $\frac{1}{\sqrt{401}}(14, 3, -14)$.

Find a Unit Vector in the Opposite Direction of U (−14,−3,14)( - 14 , - 3,14 )(−14,−3,14)

Find a Unit Vector in the Opposite Direction of U $( - 14 , - 3,14 )$