Find a unit vector in the direction of u $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$
A) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { \sqrt { 126 } } { 126 } ( 10 i + 5 j - k )$
B) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 126 } { \sqrt { 126 } } ( 10 i + 5 j - k )$
C) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { \sqrt { 126 } } { 126 } ( 10 i + 5 j - k )$
D) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 1 } { 126 } ( 10 i + 5 j - k )$
E) $\frac { u } { \| \mathbf { u } \| } =$ $\sqrt { 126 } ( 10 i + 5 j + k )$

Question

Find a unit vector in the direction of u  $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$ 
A) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { \sqrt { 126 } } { 126 } ( 10 i + 5 j - k )$
B) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 126 } { \sqrt { 126 } } ( 10 i + 5 j - k )$
C) $\frac { u } { \| \mathbf { u } \| } =$ $- \frac { \sqrt { 126 } } { 126 } ( 10 i + 5 j - k )$
D) $\frac { u } { \| \mathbf { u } \| } =$ $\frac { 1 } { 126 } ( 10 i + 5 j - k )$
E) $\frac { u } { \| \mathbf { u } \| } =$ $\sqrt { 126 } ( 10 i + 5 j + k )$

Quizplus · Accepted Answer

The magnitude of $\mathbf{u}$ is $\sqrt{10^2 + 5^2 + (-1)^2} = \sqrt{100 + 25 + 1} = \sqrt{126}$. A unit vector in the direction of $\mathbf{u}$ is obtained by dividing $\mathbf{u}$ by its magnitude, which gives $\frac{1}{\sqrt{126}}(10\mathbf{i} + 5\mathbf{j} - \mathbf{k})$, matching choice A after simplifying the fraction.

Find a Unit Vector in the Direction of U u=10i+5j−k\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }u=10i+5j−k

Find a Unit Vector in the Direction of U $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$