Question

Find a unit vector parallel to the resultant of the vectors ⃗ = 2cap − cap − 3cap and ⃗⃗ = 3icap + 4jcap − 2

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

$\vec{a} = 2 \hat{\imath} - 7 \hat{\jmath} - 3 \hat{k}$

$\vec{b} = 3 \hat{\imath} + 4 \hat{\jmath} - 2 \hat{k}$

So

$\vec{a} + \vec{b} \: = 5 \hat{\imath} - 3\hat{\jmath} - 5 \hat{k}$

Now

$|\vec{a} + \vec{b} \:| \: = \sqrt{25 + 9 + 25} = \sqrt[]{59}$

So the required unit vector parallel to the resultant of the vectors

$= \frac{(\vec{a} + \vec{b} \:)}{|\vec{a} + \vec{b} \:|} = \frac{1}{ \sqrt{59} } (5 \hat{\imath} - 3\hat{\jmath} - 5 \hat{k} )$

$</p><p></p><p>\displaystyle\textcolor{red}{Please \: Mark \: it \: Brainliest}$

Answer 2

Explanation:

\vec{a} = 2 \hat{\imath} - 7 \hat{\jmath} - 3 \hat{k}

a

=2

ı

^

−7

ȷ

^

−3

k

^

\vec{b} = 3 \hat{\imath} + 4 \hat{\jmath} - 2 \hat{k}

b

=3

ı

^

+4

ȷ

^

−2

k

^

So

\vec{a} + \vec{b} \: = 5 \hat{\imath} - 3\hat{\jmath} - 5 \hat{k}

a

+

b

=5

ı

^

−3

ȷ

^

−5

k

^

Now

|\vec{a} + \vec{b} \:| \: = \sqrt{25 + 9 + 25} = \sqrt[]{59}∣

a

+

b

∣=

25+9+25

=

59

So the required unit vector parallel to the resultant of the vectors

= \frac{(\vec{a} + \vec{b} \:)}{|\vec{a} + \vec{b} \:|} = \frac{1}{ \sqrt{59} } (5 \hat{\imath} - 3\hat{\jmath} - 5 \hat{k} )=

∣

a

+

b

∣

(

a

+

b

)

=

59

1

(5

ı

^

−3

ȷ

^

−5

k

^

)