Find a unit vector in the direction opposite of u. $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$
A) $\frac { 98 \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
B) $- \frac { \sqrt { 98 } } { 9 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
C) $- \frac { \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
D) $\frac { \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
E) $- \frac { 98 \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$

Question

Find a unit vector in the direction opposite of u. $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$ 
A) $\frac { 98 \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
B) $- \frac { \sqrt { 98 } } { 9 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
C) $- \frac { \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
D) $\frac { \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$
E) $- \frac { 98 \sqrt { 98 } } { 98 } ( 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k } )$

Quizplus · Accepted Answer

To find a unit vector in the direction opposite of $\mathbf{u}$, we first calculate the magnitude of $\mathbf{u}$ and then multiply $\mathbf{u}$ by $-1$ divided by its magnitude. The magnitude of $\mathbf{u}$ is $\sqrt{9^2 + 4^2 + (-1)^2} = \sqrt{81 + 16 + 1} = \sqrt{98}$. Thus, the unit vector in the opposite direction is $-\frac{1}{\sqrt{98}}(9\mathbf{i} + 4\mathbf{j} - \mathbf{k})$, which simplifies to $-\frac{\sqrt{98}}{98}(9\mathbf{i} + 4\mathbf{j} - \mathbf{k})$.

Find a Unit Vector in the Direction Opposite of U u=9i+4j−k\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }u=9i+4j−k

Find a Unit Vector in the Direction Opposite of U $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$