Question

Find the scalar and vector projections of b onto a. a=[1,2], b=[-4,1]

Answer 1

we have,

a=[1,2], b=[-4,1]

we need to find projection of b onto a.

scalar projection

=
`(a.b)/(|a|)`

=
`((1,2).(-4,1))/(√(1^2+2^2))`

=
`(1* (-4)+2* 1)/(√(1^2+2^2))`

=
`(-2)/(√(5))`

now, vector projection

=
`(a.b)/(|a|^2).a`

=
`((1,2).(-4,1))/((√(1^2+2^2))^2).(1,2)`

=
`(1* (-4)+2* 1)/(5).(1,2)`

=
`(-2)/(5).(1,2)`

=
`((-2)/(5),(-4)/(5))`