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hint: \(-4u=\langle -4(-6),-4(1)\rangle = \langle 24, -4\rangle\)
i really have no idea wow i feel dumb
please help @zzr0ck3r
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.
<34, -8> <14, 0> <14, 3> <44, -12> @UsukiDoll @ganeshie8 these are my options
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>
now what's -5 x 2 and 2 x 2
-10 and 4 @UsukiDoll
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> \[
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
one of my option is 14,0 is that the answer?
u vector \[
v vector \[ \]
u+v vector \[u_1+v_1,u_2+v_2+...u_n+v_n\]
wait so was i right? @UsukiDoll
yes .. 24-10 = 14 and -4+4 = 0 your u+v vector is <14,0>
can u help me with another one? @UsukiDoll
Let u = <-9, 4>, v = <8, -5>. Find u - v. <-1, -1> <-13, 13> <-17, 9> <-4, -4>
ok this is similar to the addition vector only we are dealing with subtraction u vector \[
so... we just have to match labels since we're not multiplying this time.
so what do i do next? can u take me step by step with numbers? @UsukiDoll
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=
Therefore, \[u_1=-9,u_2 = 4\]
similarly for the v vector v= <8,-5> there are only two terms in our v vector, so we have something like \[v=
\[v_1 = 8,v_2=-5\]
so its -1 and -1 rights?
now we have to do subtraction, which is finding the u-v vector which is in the form \[u-v=
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 \[u-v=
\] or in this situation just
can you help me with another ? @UsukiDoll
but did you get the final answer first?
yes it was -1,-1 @UsukiDoll
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>
the previous answer isn't right \[u-v = <-9-8, 4-(-5)>\] please try again before we can move further.
what's -9-8? and what's 4-(-5) (distribute the negative)
there we go :)
so for the next question we are dealing with dot product
\[u \cdot v =
i think the answer is <-10, -4, -12> @UsukiDoll
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>
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
I'm with another question atm.