Given that `vecu = hati + 2hatj + 3hatk , vecv = 2hati + hatk + 4hatk , vecw = hati + 3hatj + 3hatk and (vecu.vecR - 15) hati + (vecc. vecR - 30) hatj + (vecw . vec- 20) veck = vec0`. Then find the greatest integer less than or equal to `|vecR|`.

Answer

6

Explanation

Let `vecR = xhati +yhatij +zhatk`
`vecu =hati- 2hatj + 3hatk,vecv = 2hati + hatj + 4hatk, hatw=hati+3hatj+3hatk`
`(vecu.vecR-15)hati+(vecv.vecR-30)hatj+ (vecw .vecR-25)hatk=hat0`
So `vecu.vecR= 15 Rightarrow x -2y + 3z=15` (i)
`vecv.vecR = 30 Rightarrow 2x + y + 4z = 30` (ii)
`vecw.vecR= 25 Rightarrow x + 3y + 3z = 25` (iii)
solving, we get
x=4
y=2
z=5