Question

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

Answer 1

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

Answer 2

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

Answer 3

So it would start off like this?....

(1.6i + 3.3j) (-2.1i -0.5j)
= -3.36 -6.93 -1.65 -0.8

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

correction*
whenever you're taking the dot product of perpendicular vectors, the product = 0

i , j and k are perpendicular vecotrs

Answer 8

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)
=...

Answer 9

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

Answer 10

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!

Answer 11

and for the denominator its magnitude of v
= \(\sqrt {2.1^2+0.5^2} = .. \)

there is no need of doing complex divisions :)

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

About -2.32

Answer 16

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 !

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

so unit vector along v = (-2.1i -0.5j)/ 2.16

and your projection will be -2.32 times the above answer

Answer 22

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

Answer 23

what do u get after multiplying that with -2.32?

Answer 24

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

Answer 25

two negatives become positive!

and you can approximate 2.25 to 2.3 and 0.53 to 0.5 :)

Answer 26

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

Answer 27

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

Answer 28

yes, correct!
good work :)

Answer 29

Thank you for your help. :)

Answer 30

most welcome ^_^