Find a unit vector that has the same direction as the vector $\langle 2,2,1 \rangle$ .
A) $\langle 1,1,1 \rangle$
B) $\langle 1,0,0 \rangle$
C) $\langle 0,1,0 \rangle$
D) $\langle 0,0,1 \rangle$
E) $\langle 1,1,0 \rangle$
F) $\left\langle \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 } \right\rangle$
G) $\left\langle \frac { 1 } { 2 } , \frac { 1 } { 2 } , 1 \right\rangle$
H) $\left\langle \frac { 1 } { 3 } , \frac { 1 } { 3 } , 1 \right\rangle$

Question

Find a unit vector that has the same direction as the vector $\langle 2,2,1 \rangle$ .
A) $\langle 1,1,1 \rangle$ 
B) $\langle 1,0,0 \rangle$ 
C) $\langle 0,1,0 \rangle$ 
D) $\langle 0,0,1 \rangle$ 
E) $\langle 1,1,0 \rangle$ 
F) $\left\langle \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 } \right\rangle$ 
G) $\left\langle \frac { 1 } { 2 } , \frac { 1 } { 2 } , 1 \right\rangle$ 
H) $\left\langle \frac { 1 } { 3 } , \frac { 1 } { 3 } , 1 \right\rangle$

Quizplus · Accepted Answer

To find a unit vector in the same direction as $\langle 2,2,1 \rangle$, divide each component by the magnitude of the vector. The magnitude is $\sqrt{2^2 + 2^2 + 1^2} = \sqrt{9} = 3$. Dividing each component by 3 gives $\left\langle \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 } \right\rangle$, which is a unit vector in the same direction.

Find a Unit Vector That Has the Same Direction as the Vector