Answer:
The ascending order is:
2) ,4), 5) ,1) ,6) ,3)
Step-by-step explanation:
We are given u=<9,-2> , v=<-1,7> , w=<-5,-8>
The magnitude of some vector <a,b> is given by: [tex]\sqrt{a^2+b^2}[/tex]
we will find the representation of each of the vectors in order to calculate their magnitudes and arrange them in the ascending order.
1) [tex]\dfrac{-1}{2}u+5v[/tex]
on calculating the value of this operation:
[tex]\dfrac{-1}{2}<9,-2>+5<-1,7>=<\dfrac{-9}{2},1>+<-5,35>\\ \\=<\dfrac{-19}{2},36>[/tex]
Hence, the magnitude of [tex]\dfrac{-1}{2}u+5v[/tex] is:
37.2324
2) [tex]\dfrac{1}{6}(u+2v-w)[/tex]
the value of this operation is given as:
[tex]\dfrac{1}{6}(<9,-2>+<-2,14>-<-5,-8>)\\ \\=\dfrac{1}{6} (<9,-2>+<-2,14>+<5,8>)\\\\=\dfrac{1}{6} (<12,20>)\\\\=<2,\dfrac{10}{3}>[/tex]
Hence, the magnitude of [tex]\dfrac{1}{6}(u+2v-w)[/tex] is:
3.8873
3) [tex]\dfrac{5}{2}u-3w[/tex]
The value of this operation is given as:
[tex]\dfrac{5}{2}<9,-2>-3<-5,-8>\\\\=<\dfrac{75}{2},19>[/tex]
Hence, the magnitude of [tex]\dfrac{5}{2}u-3w[/tex] is:
42.0387
4) [tex]u-\dfrac{3}{2}v+2w[/tex]
The value of this operation is given as:
[tex]<9,-2>-\dfrac{3}{2}<-1,7>+2<-5,-8>\\ \\=<\dfrac{1}{2},\dfrac{-15}{2}>[/tex]
Hence, the magnitude of [tex]u-\dfrac{3}{2}v+2w[/tex] is:
7.5166
5) [tex]-4v+\dfrac{1}{2}w[/tex]
the value of the operation is given as:
[tex]-4<-1,7>+\dfrac{1}{2}<-5,-8>\\\\=<\dfrac{3}{2},-32>[/tex]
Hence, the magnitude of [tex]-4v+\dfrac{1}{2}w[/tex] is:
32.0351
6) [tex]3u-v-\dfrac{5}{2}w[/tex]
The value of this operation is:
[tex]3<9,-2>-<-1,7>-\dfrac{5}{2}<-5,-8>\\ \\=<\dfrac{81}{2},7>[/tex]
Hence the magnitude of [tex]3u-v-\dfrac{5}{2}w[/tex] is:
40.5863
On Arranging the above operations on the basis of their magnitude in ascending order we get the order as:
2) ,4), 5) ,1) ,6) ,3)
Answer: the above answer is correct
Step-by-step explanation: I got this right on Edmentum
