find the projection of the vector `hati+3hatj=7hatk` on the vector `7hati-hatj+8 hatk`

Options

A. `(60)/(sqrt(122))`
B. `(30)/(sqrt(144))`
C. `(60)/(sqrt(114))`
D. `(60)/(sqrt(111))`

Answer

C

Explanation

Let ` a = hati + 3 hatj + 7 hatk` and ` 7 hati - hatj +8hatk,` then projection of a on b is given by
` (a.b) /(|b|)=[((hati +3hatj +7 hatk).(7 hati -hatj+8hatk))/(sqrt(7)^(2)+(-1)^(2)+8^(2))]`
`=[(1xx7+3xx(-1)+7xx8)/((sqrt(49)+1+64))]=(7-3+56)/(sqrt(114))=(60)/(sqrt(114))`