Question

Which components are a possible representation of vector u if ||-4u|| ≈ 14.42?

a.<3.-2
b.<-1,4>
c.<2,2>
d.<-2,-4>

Answer 1

`<3,-2>`

Explanation:

Check for each vector

`u=<3,-2>\\4u=<12,-8>\\||4u||=√(12^2+8^2)\\=√(208) \\=14.42`

Hence this is the required vector.

`u=<-1,4>\\4u=<-4,16>\\||4u||=√(4^2+16^2)=16.49`

`u=<2,2>\\4u=<8,8>\\||4u||=√(8^2+8^2)=11.31`

`u=<-2,4>\\4u=<-8,16>\\||4u||=√(8^2+16^2)=17.889`

Hence required vector
`=<3,-2>`