Question

What is the projection of `(32i-38j-12k)` onto `(18i -30j -12k)`?

Answer 1

`vec c= <24,47i,-40,79j,-16,32k>`

Explanation:

`vec a= <32i,-38j,-12k>`
`vec b= <18i,-30j,-12k>`
`vec a * vec b =18*32+38*30+12*12=`
`vec a * vec b=576+1140+144=1860`
`|b|=sqrt(18^2+30^2+12^2)`
`|b|=sqrt(324+900+144)`
`|b|=sqrt1368`
`vec c=(vec a*vec b)/(|b|*|b|)*vec b`
`vec c=1860/(sqrt 1368 *sqrt 1368)<18i,-30j,-12k>`
`vec c=1860/1368<18i,-30j,-12k>`
`vec c= <(1860*18i) /1368, (-1860*30j)/1368,(-1860*12k)/1368>`
`vec c= <24,47i,-40,79j,-16,32k>`