Question

Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v.
@ganeshie8 @hero @dan815 @pooja195 @triciaal @loser66 @wio @luigi0210

Answer 1

hint: \(-4u=\langle -4(-6),-4(1)\rangle = \langle 24, -4\rangle\)

Answer 2

i really have no idea
wow i feel dumb

Answer 3

@zzr0ck3r

Answer 4

please help @zzr0ck3r

Answer 5

adding vectors is in the form
\[u_1+v_1,u_2+v_2,...u_n+v_n \]
but before we can do that we need to distribute the -4 on the u vector and distribute the 2 on the v vector.

Answer 6

<34, -8>
<14, 0>
<14, 3>
<44, -12>
@UsukiDoll @ganeshie8
these are my options

Answer 7

zzrocker already did the distribute -4 all over the u vector
now we have to distribute 2 all over the v vector

2<-5,2>

Answer 8

now what's -5 x 2 and 2 x 2

Answer 9

-10 and 4 @UsukiDoll

Answer 10

ok cool... so our 2v is <-10,4>

so let's add them together

zzrocker already did -4u which was <24,-4>

so now we have
<24,-4> +<-10,4>
\[<u_1,u_2> + <v_1,v_2>\]
so we have \[u_1 = 24, u_2 = -4, v_1 = -10, v_2 = 4\]
but our final answer has to be in the form
\[<u_1+v_1,u_2+v_2> \]

Answer 11

one of my option is 14,0
is that the answer?

Answer 12

@UsukiDoll

Answer 13

u vector \[<u_1,u_2...u_n>\]
v vector \[<v_1,v_2,...v_n>\]
u+v vector \[u_1+v_1,u_2+v_2+...u_n+v_n\]

Answer 14

\[<24-10,-4+4 >\]

Answer 15

wait so was i right? @UsukiDoll

Answer 16

yes .. 24-10 = 14 and -4+4 = 0
your u+v vector is <14,0>

Answer 17

can u help me with another one? @UsukiDoll

Answer 18

sure

Answer 19

Let u = <-9, 4>, v = <8, -5>. Find u - v.

<-1, -1>
<-13, 13>
<-17, 9>
<-4, -4>

Answer 20

ok this is similar to the addition vector only we are dealing with subtraction
u vector
\[<u_1,u_2,...u_n> \]
v vector
\[<v_1,v_2,...v_n >\]
u-v vector
\[<u_1-v_1,u_2-v_2,....u_n-v_n>\]

Answer 21

so... we just have to match labels since we're not multiplying this time.

Answer 22

so what do i do next? can u take me step by step with numbers? @UsukiDoll

Answer 23

sure

Answer 24

let's start with the u vector
u=<-9,4>
recall that our u vector is in the form of
\[u_1,u_2,...u_n \]
since there are only 2 terms in our u vector, we have something like
\[u=<u_1,u_2>\]
Therefore, \[u_1=-9,u_2 = 4\]

Answer 25

similarly for the v vector
v= <8,-5>
there are only two terms in our v vector, so we have something like
\[v=<v_1,v_2> \]
Therefore,
\[v_1 = 8,v_2=-5\]

Answer 26

so its -1 and -1 rights?

Answer 27

now we have to do subtraction, which is finding the u-v vector which is in the form
\[u-v=<u_1-v_1,u_2-v_2...u_n-v_n>\]

Answer 28

only one of them will be -1. Recall these values
\[u_1=-9,u_2 = 4 \]
\[v_1 = 8,v_2=-5 \]

now our u-v vector is in the form
\[u-v=<u_1-v_1,u_2-v_2...u_n-v_n>\] or in this situation just
\[u-v=<u_1-v_1,u_2-v_2>\]

Answer 29

can you help me with another ? @UsukiDoll

Answer 30

but did you get the final answer first?

Answer 31

yes it was -1,-1 @UsukiDoll

Answer 32

Evaluate the expression.
r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6>
v ⋅ w

<-18, 14, -2>
-26
1
<-10, -4, -12>

Answer 33

the previous answer isn't right
\[u-v = <-9-8, 4-(-5)>\] please try again before we can move further.

Answer 34

what's -9-8?
and what's 4-(-5) (distribute the negative)

Answer 35

-17,9

Answer 36

there we go :)

Answer 37

so for the next question we are dealing with dot product

Answer 38

\[u \cdot v =<u_1v_1,u_2v_2,...u_nv_n> \]

Answer 39

i think the answer is <-10, -4, -12> @UsukiDoll

Answer 40

only it's just \[v \cdot w \]
where v = <2,2,-2 > and w = <-5,-2,6>
yeah you're right
\[v_1=2,v_2=2,v_3=-2...w_1=-5,w_2=-2,w_3=6\]
\[v_1w_1=-10,v_2w_2=-4,v_3w_3=-12\]
<-10,-4,-12>

Answer 41

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

B = 46°, a = 12, b = 11

A = 38.3°, C = 95.7°, c = 8; A = 141.7°, C = 84.3°, c = 8
A = 51.7°, C = 82.3°, c = 8; A = 128.3°, C = 5.7°, c = 8
A = 38.3°, C = 95.7°, c = 15.2; A = 141.7°, C = 84.3°, c = 15.2
A = 51.7°, C = 82.3°, c = 15.2; A = 128.3°, C = 5.7°, c = 1.5
@UsukiDoll

Answer 42

I'm with another question atm.