Question

Which components are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15?

<1,-9>
<-3,4>
<4,5>
<-5,-3>
<0,-5>

Answer 1

Answer: <-3,4> and <0,-5>

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

Answer 2

<-3,4>

<0,-5>

Explanation:

|-3w| = 15

3|-w| = 3|w| = 15

|w| =
`(15)/(3)`

|w| = 5

• If vector w is represented by <1,-9>

Then |w| =
`\sqrt{(1)^(2)+(-9)^(2)}=√(1+81)=√(82)\\eq5` .

Therefore this is not possible.

• If vector w is represented by <-3,4>

Then |w| =
`\sqrt{(-3)^(2)+(4)^(2)}=√(9+16)=√(25)=5` .

Therefore this is possible.

• If vector w is represented by <4,5>

Then |w| =
`\sqrt{(4)^(2)+(5)^(2)}=√(16+25)=√(41)\\eq5` .

Therefore this is not possible.

• If vector w is represented by <-5,-3>

Then |w| =
`\sqrt{(-5)^(2)+(-3)^(2)}=√(25+9)=√(34)\\eq5` .

Therefore this is not possible.

• If vector w is represented by <0,-5>

Then |w| =
`\sqrt{(0)^(2)+(-5)^(2)}=√(0+25)=√(25)=5` .

Therefore this is possible.

(NOTE : if z vector is represented by <x,y> then |z| =
`\mathbf{\sqrt{x^(2)+y^(2)}}` )