Question

3 part question

Answer 1

a) is asking for the magnitude of v1 and v2

remember that magnitude = sqrt(x^2 + y^2)

so start with the coordinates of v1 first

Answer 2

oh I would recommend leaving the results in radical form rather than decimal form, so your answer should have the radical symbol in it

Answer 3

magnitude = sqrt(x^2 + y^2)
=sqrt(2^2+-6^2)
=4isqrt2


magnitude= sqrt(x^2 + y^2)
=sqrt(-4^2+7^2)
=sqrt33

Answer 4

you have to be very careful with negative signs

if you want to square a negative # then it must be written

(-x)^2 not -x^2

Answer 5

magnitude = sqrt(x^2 + y^2)
=sqrt(2^2+(-6)^2)
=2sqrt10


magnitude= sqrt(x^2 + y^2)
=sqrt((-4)^2+7^2)
=sqrt65

Answer 6

awesome

now for b) the unit vector is simply the vector divided by the magnitude

for example, the unit vector in the direction of v1 = v1/ magnitude of v1 = ?

Answer 7

(2,-6)/2sqrt10

Answer 8

good, but "distribute" the division across both coordinates, ex:

2/(2*sqrt(10) and (-6)/(2sqrt10)

Answer 9

anyway, you just need to simplify these to get

(1/sqrt(10) and (-3sqrt(10)

and put these together to get the unit vector

(1/sqrt(10), -3sqrt(10))

can you try to repeat this process with vector v2?

Answer 10

yes i will

Answer 11

*oh btw that last vector should be (1/sqrt(10), -3/sqrt(10))
whoops

Answer 12

so vector 2 = (-4,7) right

the magntitude = sqrt(65)

so you just need to divide each coordinate by sqrt(65) to get the unit vector

Answer 13

(-4)/sqrt(65) and 7/sqrt65

Answer 14

like that

Answer 15

yes, now put them together as a vector to get the new unit vector

Answer 16

((-4)/sqrt(65) , 7/sqrt65)

Answer 17

awesome

Answer 18

alright now for the graph, to plot a vector, assume it starts at the origin (unless otherwise stated), plot a point at the vector coordinates, then draw an arrow pointing from the origin to the point

(probably easier to see as a picture so:

Answer 19

then the arrow:

Answer 20

can you try repeating with v2?

Answer 21

the coordinates of v2 are (-4,7) so we just gotta plot (-4,7) and draw the arrow

Answer 22

then to add 2 vectors we use the tail to tip method

Answer 23

in this case, we would move v2 so that the tail of v2 is at the tip of v1

Answer 24

and that's it

Answer 25

sorry im drawing this all out which is why i am not responding tht fast

Answer 26

you don't need the curvy arrow (that's just for you to see how the vector moved)

make sure to label the three vectors as v1, v2, and v1 + v2 respectively