Question

Find the angle made by the following vector with the coordinates axes:
`(hati+hatj+hatk)`
`(hatj-hatk)`
`(hati-4hatj+8hatk)`

Answer 1

Correct Answer - (i) `cos^(-1)((1)/(sqrt3)),cos^(-1)((1)/(sqrt3)),cos^(-1)((1)/(sqrt3))`
(ii) `(pi)/(2),(pi)/(4),(3pi)/(4)`
(iii) `cos^(-1)""((1)/(9)),cos^(-1)((4)/(9)),cos^(-1)((8)/(9))`
(i) Let `veca=hati-hatj+hatk`.
`cosalpha=((hati-hatj+hatk)*hati)/(|hati-hatj+hatk||hati|)=(1)/(sqrt3),cosbeta=((hati-hatj+hatk)*hatj)/(|hati-hatj+hatk||hatj|)=(-1)/(sqrt3)`
and `cosgamma=((hati-hatj+hatk)*hatk)/(|hati-hatj+hatk||hatk|)=(1)/(sqrt3)`.