Question

u = -4i + 1j and v = 4i + 1j; Find .||u+V|| the answer is u+v=2j

Answer 1

my teacher siad i was wrong

Answer 2

\(\|u+v\|\) represents the length of vector \(u+v\)

Answer 3

what you had there is just the vector \(u+v\)
but your teacher wants its length

Answer 4

ohh ok

Answer 5

how does vector 2j look ?

Answer 6

You are already given where vector u and vector v are pointing at, the distance between these points can be found using distance formula

Answer 7

how do i do that

Answer 8

wait sorry nevermind I messed up, forget that figure ok

Answer 9

for a vector
\[\vec a=x \hat i+y \hat j+z \hat k\]
It's magnitude is given by
\[|\vec a|=a=\sqrt{x^2+y^2+z^2}\]
so for
\[|\vec u + \vec v|=\sqrt{?^2+?^2+?^2}\]

Answer 10

your vector
\[\vec u + \vec v =0\hat i+2\hat j+0\hat k\]

Answer 11

im so counfuzzled this is why i dont do math lol

Answer 12

ok I will try to explain

Answer 13

\[\vec a=x \hat i+y \hat j\]

Answer 14

You can think of it has moving x amount along x-axis(in the direction of i hat) and moving y units along y-axis (in the direction of j hat)

Answer 15

Do you understand this much?

Answer 16

so far

Answer 17

Now consider
the triangle

How can you solve for the question mark?

Answer 18

It's a right triangle

Answer 19

umm i needa find the ? how do i do that

Answer 20

Yep, remember the good ol pythagorus thm?

Answer 21

i do put i never could do it properly

Answer 22

\[c^2=a^2+b^2\]
\[c=\sqrt{a^2+b^2}\]

Answer 23

remember that?

Answer 24

yes i do

Answer 25

Then if your sides are of x and y length, then what will be the "c" in that case?

Answer 26

instead of a and b, we have x and y

Answer 27

you there bro?