Question

given that u= 3i -2j + 3k, find the unit vector in the opposite direction to u​

Answer 1

SOLUTION

GIVEN

The given vector is

$\vec{u} = 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}$

TO DETERMINE

The unit vector in the opposite direction to

$\vec{u}$

EVALUATION

Here the given vector is

$\vec{u} = 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}$

$\therefore \: \: | \: \vec{u} \: | = 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}$

$= |3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}|$

$= \sqrt{9 + 4 + 9}$

$= \sqrt{22}$

So the unit vector in the direction to $\vec{u}$

$\displaystyle \: = \frac{ \vec{u}}{ | \: \vec{u} \: | }$

$\displaystyle \: = \frac{ 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}}{ \sqrt{22} }$

Hence the required unit vector in the opposite direction to $\vec{u}$

$\displaystyle \: = - \frac{ 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}}{ \sqrt{22} }$

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Answer 2

SOLUTION

GIVEN

The given vector is

$\vec{u} = 3 \hat{ \imath} - 2 \hat{ \jmath} + 3 \hat{k}$

TO DETERMINE

The unit vector in the opposite direction to

u

EVALUATION

Here the given vector is

u =3 −2j +3k

∴∣u∣=3i −2j +3k

=∣3i−2j +3k∣

= √9+4+9

= √22

So the unit vector in the direction to

u

u/|u|

3i - 2j + 3k/√22

Hence the required unit vector in the opposite direction to

u

= - 3i - 2j + 3k/√22