If `vec(a) = 3 hat(i) + 2 hat(k) , vec(b) = 3hat(j) - hat(k)` and `vec(c ) = hat(i) + hat(j) + hat(k)`. Find `( vec(a) xx vec(b)). vec(c )`.

Explanation

`vec(a) xx vec(b) = |(1 , - , +) ,(hat(i) , hat(j) , hat(k)),(3 , 0 , 2), (0 , 3 , -4)|`
` = hat(i) ( 0 - 6) - hat(j) ( - 12 - 0) + hat(k) ( 9 - 0)`
` = - 6 hat(i) + 12 hat(j) + 9 hat(k)`
`(vec(a) xx vec(b)) . vec(c ) = ( - 6 hat (i) + 12 hat(j) + 9 hat(k)) . (hat(i) + hat(j) + hat(k))`
`= - 6 + 12 + 9 = 15`