Question

Vector u= <9,-2> v=<-1,7> w=<-5,-8> arrange the vector operations in ascending order of their magnitudes of their resultant vectors

Operations:
1.) -1/2u + 5v
2.) 1/6 (u+2v-w)
3.)5/2u-3w
4.)u-3/2v+2w
5.)-4v+1/2w
6.)3u-v-5/2w

Answer 1

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:  $\sqrt{a^2+b^2}$

we will find the representation of each of the vectors in order to calculate their magnitudes and arrange them in the ascending order.

1) $\dfrac{-1}{2}u+5v$

on calculating the value of this operation:

$\dfrac{-1}{2}<9,-2>+5<-1,7>=<\dfrac{-9}{2},1>+<-5,35>\\  \\=<\dfrac{-19}{2},36>$

Hence, the magnitude of  $\dfrac{-1}{2}u+5v$ is:

37.2324

2) $\dfrac{1}{6}(u+2v-w)$

the value of this operation is given as:

$\dfrac{1}{6}(<9,-2>+<-2,14>-<-5,-8>)\\ \\=\dfrac{1}{6} (<9,-2>+<-2,14>+<5,8>)\\\\=\dfrac{1}{6} (<12,20>)\\\\=<2,\dfrac{10}{3}>$

Hence, the magnitude of  $\dfrac{1}{6}(u+2v-w)$ is:

3.8873

3) $\dfrac{5}{2}u-3w$

The value of this operation is given as:

$\dfrac{5}{2}<9,-2>-3<-5,-8>\\\\=<\dfrac{75}{2},19>$

Hence, the magnitude of  $\dfrac{5}{2}u-3w$ is:

42.0387

4) $u-\dfrac{3}{2}v+2w$

The value of this operation is given as:

$<9,-2>-\dfrac{3}{2}<-1,7>+2<-5,-8>\\ \\=<\dfrac{1}{2},\dfrac{-15}{2}>$

Hence, the magnitude of  $u-\dfrac{3}{2}v+2w$ is:

7.5166

5) $-4v+\dfrac{1}{2}w$

the value of the operation is given as:

$-4<-1,7>+\dfrac{1}{2}<-5,-8>\\\\=<\dfrac{3}{2},-32>$

Hence, the magnitude of $-4v+\dfrac{1}{2}w$ is:

32.0351

6) $3u-v-\dfrac{5}{2}w$

The value of this operation is:

$3<9,-2>-<-1,7>-\dfrac{5}{2}<-5,-8>\\ \\=<\dfrac{81}{2},7>$

Hence the magnitude of  $3u-v-\dfrac{5}{2}w$ 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 2

Answer: the above answer is correct

Step-by-step explanation: I got this right on Edmentum