Question

Vectors: Let V1 = -6.2i + 8.2j and V2 = -4.9j + 4.3j
Determine the direction of V1 and V2.

Answer 1

The questions before that ask for the magnitude of both vectors, I've gotten 10.28 and 6.5

Answer 2

direction is measured from the +x axis right?

Answer 3

10.28 = V1 and .6.5 = V2

Answer 4

yes

Answer 5

and these vector specifically are just the same as a point on the plane; to which you can use tan(t) = y/x

Answer 6

or j/i as the case may be

Answer 7

Actually its not, its saying that the direction angle is counterclockwise from the positive x direction for both vectors. So i would use arctan right?

Answer 8

right, its measured from the +x axis; clockwise tends to be a given in that as a default

Answer 9

arctan(j/i)

yes. and since we are in the 2nd quadrant we will have to modify it as such

Answer 10

your answer in arc tan will give you the reference angle; so 180 - reference should give us the degrees we want

Answer 11

well; pi - arctan(j/i) = radian measure

Answer 12

arctan is restricted to give us this angle here so we need to use that to our best abilities

does that make sense?

Answer 13

yes it does

Answer 14

so arctan gives us "a" which is negative sooo; pi + a should result in the direction angle we desire

Answer 15

or if your using vectors then youre prolly aware that cos(t) = a.b/|a||b|

where "a" can be our given vector; and b = <1,0>

Answer 16

so the arctan of vector 1 is tan = 8.2/-6.2 = arctan(-1.322) = -52.895

and pi-arctan(-1.322) = 56.03

Answer 17

<-6.2, 8.2>
< 1 , 0 > ; |b| = 1 sooo
------------
-6.2 = a.b

cos(t) = -6.2/|a|

t = arccos(-6.2/|a|)

Answer 18

add alpha; should got about 127.1 degrees

Answer 19

2. somehting rads

Answer 20

To answer your third to last post, yes I am familar with that formula.

Answer 21

then its prolly easier to do; no need to evaluate for quadrants or pi s or none of that

Answer 22

\[angle=arccos(\frac{vi}{|v|})\]

Answer 23

where vi is the x component (the i part) of your given vector

Answer 24

So in your formula some posts above, for "a.b" did you mean "a*b" (a times b)?

Answer 25

and what is alpha?

Answer 26

there is no multiplication of vectors defined; they refer to it as a dot product.

take 2 vectors, u and v

u = <a,b>
v = <c,d>

the dot product of u and v is defined as:

<a,b>
<c,d>
-----
ac+bd multiply component parts and add the results

Answer 27

Okay, well I actually think i got what you meant before using the arctangent method. For the first vector, I took the arctan of (8.2/-6.2)=-52.90

Now 180 - (-52.90) gave me about 127. Is this right?