Find a unit vector in the direction of u. $\mathbf { u } = - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k }$
A) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { \sqrt { 270 } } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
B) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { \sqrt { 270 } } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
C) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 270 } { \sqrt { 270 } } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
D) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 270 } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
E) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { 270 } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$

Question

Find a unit vector in the direction of u.  $\mathbf { u } = - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k }$ 
A) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { \sqrt { 270 } } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
B) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { \sqrt { 270 } } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
C) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 270 } { \sqrt { 270 } } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
D) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 270 } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$
E) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { 270 } { 270 } ( - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k } )$

Quizplus · Accepted Answer

The magnitude of vector $\mathbf{u}$ is $\sqrt{(-5)^2 + 7^2 + 14^2} = \sqrt{25 + 49 + 196} = \sqrt{270}$. A unit vector in the direction of $\mathbf{u}$ is given by dividing $\mathbf{u}$ by its magnitude, which is $\frac{1}{\sqrt{270}}(-5\mathbf{i} + 7\mathbf{j} + 14\mathbf{k})$, matching option A.

Find a Unit Vector in the Direction of U u=−5i+7j+14k\mathbf { u } = - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k }u=−5i+7j+14k

Find a Unit Vector in the Direction of U $\mathbf { u } = - 5 \mathbf { i } + 7 \mathbf { j } + 14 \mathbf { k }$