Question

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

Answer 1

Answer:

<-3,4>

<0,-5>

Step-by-step explanation:

|-3w| = 15

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

|w| = $\frac{15}{3}$

|w| = 5

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

Then |w| = $\sqrt{(1)^{2}+(-9)^{2}}=\sqrt{1+81}=\sqrt{82}\neq5$ .

Therefore this is not possible.

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

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

Therefore this is possible.

• If vector w is represented by <4,5>

Then |w| = $\sqrt{(4)^{2}+(5)^{2}}=\sqrt{16+25}=\sqrt{41}\neq5$ .

Therefore this is not possible.

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

Then |w| = $\sqrt{(-5)^{2}+(-3)^{2}}=\sqrt{25+9}=\sqrt{34}\neq5$ .

Therefore this is not possible.

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

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

Therefore this is possible.

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