Question

Find the scalar and vector projections of b onto a. a=[2,-1,4], b=[0,1,1/2]

Answer 1

we have,

a=[2,-1,4], b=[0,1,1/2]

we need to find projection of b onto a.

scalar projection

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

=
`((2,-1,4).(0,1,1/2))/(√(2^2+(-1)^2+4^2))`

=
`(2* (0)+(-1)* 1 + 4* 0.5)/(√(2^2+(-1)^2+4^2))`

=
`(1)/(√(21))`

now, vector projection

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

=
`((2,-1,4).(0,1,1/2))/((√(2^2+(-1)^2+4^2))^2).(2,-1,4)`

=
`(2* (0)+(-1)* 1 + 4* 0.5)/(21).(2,-1,4)`

=
`(1)/(21).(2,-1,4)`

=
`((2)/(21),(-1)/(21),(4)/(21))`