Let u= <4,3>. Find the unit vector in the direction of u, and write your answer in component form.

1 answer:

3 0

Take the vector u = <ux, uy> = <4, 3>.

Find the magnitude of u:

||u|| = sqrt[ (ux)^2 + (uy)^2]

||u|| = sqrt[ 4^2 + 3^2 ]

||u|| = sqrt[ 16 + 9 ]

||u|| = sqrt[ 25 ]

||u|| = 5

To find the unit vector in the direction of u, and also with the same sign, just divide each coordinate of u by ||u||. So the vector you are looking for is

u/||u||

u * (1/||u||)

= <4, 3> * (1/5)

= <4/5, 3/5>

and there it is.

Writing it in component form:

= (4/5) * i + (3/5) * j

I hope this helps. =)

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Step-by-step explanation:

Let x represent the number of nickels

Let y represent the number of quarters
—————————————————————

Value Value
Type Number of of
of of each all
Coin Coin Coin Coin
—————————————————————
Nickels | x | $0.05 | $0.05x
Quarters | y | $0.25 | $0.25y
—————————————————————
Totals 28 ——— $2.20
•••••••••••••••••••••••••••••••••••••••••••••••••

The first equation comes from the “Number of coins” column.

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—————————————————————
The second equation comes from the “value of all coins” column.

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—————————————————————
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————————————————————
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————————————————————
Checking:

24 nickels is $1.20 and 4 quarters is $1.00
That’s 28 coins.
Indeed $1.20 + $1.00 = $2.20
————————————————————

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