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Classical Mechanics

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Find a Unit Vector

CLMECH-GLXDKB

Find the unit vector $\vec{u}$ which is in the same direction as the vector $\vec { v } = 12\hat { i } -3\hat { j } +4\hat { k }$.

A

$\vec { u } =12 \cdot \hat { i } -3 \cdot \hat { j } +4 \cdot \hat { k }$

B

$\vec { u } =\frac { 12 }{ 169 } \hat { i } -\frac { 3 }{ 169 } \hat { j } +\frac { 4 }{ 169 } \hat { k }$

C

$\vec { u } =\hat { i } +\hat { j } +\hat { k }$

D

$\vec { u } =\frac { 12 }{ 13 } \hat { i } -\frac { 3 }{ 13 } \hat { j } +\frac { 4 }{ 13 } \hat { k }$

E

$\vec { u } ={\frac { 12 }{ \sqrt { 13 } } }\hat { i } -\frac { 3 }{ \sqrt { 13 } } \hat { j } +\frac { 4 }{ \sqrt { 13 } } \hat { k } $

F

$\vec { u } =\hat { i } -\hat { j } +\hat { k }$