The projection of a vector on the coordinate axes are `6,-3,2.` Find its length and direction cosines.

Explanation

If `cosα,cosβ,cosγ` are the direction cosines then
`rcosα=6,rcosβ=−3,rcosγ=2`
Squaring ,`r^2cos^2α=36,r^2cos^2β=9,r^2cos^2γ=4`
`=>r^2cos^2α+r^2cos^2β+r^2cos^2γ=36+9+4`
`=>r^2cos^2α+r^2cos^2β+r^2cos^2γ=49`
`=>r^2=49`
`=>r=7`
`∴` the direction cosines are `6/7,-3/7,2/7`