Question

Find the unit vector of the given vector a = 4i -2j +k

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Answer 1

Answer:

CORRECT QUESTION :

Present ages of Anu and Raj are in the ratio 4:5 . Eight years from now the ratio of the ages will be 5:6. Find their present ages .

Given :

Present ages of Anu and Raj are in the ratio 4:5 .

Eight years from now the ratio of the ages will be 5:6.

To Find :

Present Age of Anu and Raj .

Solution :

\longmapsto\tt{Let\:Present\:age\:of\:Anu\:be=4x}⟼LetPresentageofAnube=4x

\longmapsto\tt{Let\:Present\:age\:of\:Raj\:be=5x}⟼LetPresentageofRajbe=5x

After 8 years :

\longmapsto\tt{Age\:of\:Anu=4x+8}⟼AgeofAnu=4x+8

\longmapsto\tt{Age\:of\:Raj=5x+8}⟼AgeofRaj=5x+8

A.T.Q :

\longmapsto\tt{\dfrac{4x+8}{5x+8}=\dfrac{5}{6}}⟼

5x+8

4x+8

=

6

5

\longmapsto\tt{6(4x+8)=5(5x+8)}⟼6(4x+8)=5(5x+8)

\longmapsto\tt{24x+48=25x+40}⟼24x+48=25x+40

\longmapsto\tt{24x-25x=40-48}⟼24x−25x=40−48

\longmapsto\tt{-1x=-8}⟼−1x=−8

\longmapsto\tt\bf{x=8}⟼x=8

Value of x is 8 .

Therefore :

\longmapsto\tt{Present\:age\:of\:Anu=4(8)}⟼PresentageofAnu=4(8)

\longmapsto\tt\bf{32\:yrs}⟼32yrs

\longmapsto\tt{Present\:age\:of\:Raj=5(8)}⟼PresentageofRaj=5(8)

\longmapsto\tt\bf{40\:yrs}⟼40yrs

Answer 2

Answer:

$\frac{4i -2j +k}{\sqrt{21}}$

PLZ:

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Explanation:

unit vector of a vector is vector divided by its magnitude

magnitude of the given vector

$\sqrt{4^{2}+(-2)^{2}+1^{2} } =\sqrt{16+4+1} =\sqrt{21}$

So,the required unit vector:

$\frac{4i -2j +k}{\sqrt{21}}$