Can someone help me with some math questions? I'll fan and medal. :)

- anonymous

Can someone help me with some math questions? I'll fan and medal. :)

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- anonymous

##### 1 Attachment

- hartnn

do you know how to get projection of one vector on other?
tried to solve this?

- hartnn

Projection of vector a on vector b is
\(\LARGE \dfrac{a.b}{|b|}\)

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## More answers

- anonymous

So it would start off like this?....
(1.6i + 3.3j) (-2.1i -0.5j)
= -3.36 -6.93 -1.65 -0.8

- hartnn

note that
\(i . j \)
and \(j.i\)
both = 0
as they are perpendicular vectors!

- hartnn

so you'll only have
1.6*(-2.1) + 3.3*(-0.5) = ...

- anonymous

So just to be clear - Whenever you're multiplying the different variables in a vector, the become zero?

- hartnn

correction*
whenever you're taking the dot product of perpendicular vectors, the product = 0
i , j and k are perpendicular vecotrs

- anonymous

Got it.
So...
1.6*(-2.1) + 3.3*(-0.5)
= -3.36i -1.65j
then you divide that answer by (-2.1i -0.5j)
(-3.36i -1.65j) / (-2.1i -0.5j)
=...

- anonymous

Give me just a second on the division. I think I did something wrong.

- hartnn

so your u.v will be = 1.6*(-2.1) + 3.3*(-0.5) = ...
its a numeric value, because its a dot product
it won't have i's and j's in it!

- hartnn

and for the denominator its magnitude of v
= \(\sqrt {2.1^2+0.5^2} = .. \)
there is no need of doing complex divisions :)

- hartnn

1.6*(-2.1) + 3.3*(-0.5) = -5.01

- anonymous

So the numerator is -5.01
and the denominator is about 2.16
and you would divide that?

- hartnn

thats right
that will give you the magnitude of the projection vector :)

- anonymous

About -2.32

- hartnn

thats the magnitude,
now you only need the direction of projection vector
and since projection is along the vector 'v'
its direction will be same as that of vector v !

- hartnn

for that, you'll need to find the unit vector in the direction of v
and then mutiply the above answer to it.

- anonymous

Wouldn't "b" be the direction? (-2.1i -0.5j)

- hartnn

you need projection of vector u along vector 'v'
so its direction will be along vector 'v'
whats b and where it came form ?

- hartnn

unit vector along v = v/ |v|
and we already know |v| = 2.16

- hartnn

so unit vector along v = (-2.1i -0.5j)/ 2.16
and your projection will be -2.32 times the above answer

- anonymous

(-2.1i -0.5j)/ 2.16
Would that be (-0.97i -0.23)?

- hartnn

what do u get after multiplying that with -2.32?

- anonymous

-2.32 (-0.97i -0.23)
= (-2.25i -0.53j)

- hartnn

two negatives become positive!
and you can approximate 2.25 to 2.3 and 0.53 to 0.5 :)

- hartnn

-2.32 * -0.97 = +2.3
-2.32 * -0.23 = +0.5

- anonymous

Oops! I didn't even see the double negatives.
Thank you for catching that.
So the answer would be B. (2.3i +0.5j)

- hartnn

yes, correct!
good work :)

- anonymous

Thank you for your help. :)

- hartnn

most welcome ^_^

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