There are two vectors `vecA= 3hati+hatj and vecB=hatj+2hatk`. For these two vectors -
(a) If `vecA & vecB` are the adjacent sides of a parallelogram then find the magnitude of its area.
(b) Find a unit vector which is perpendicular to both `vecA & vecB`.

Answer

(a) 7 units
(b) `(2)/(7)hati- (6)/(7)hatj+ (3)/(7)hatk`

Explanation

(a) Area of the parallelogram `= |vecA xx vecB| = |{:(hati,,hatj,,hatk),(3,,1,,0),(0,,1,,2):}|`
`" "= |2hati-6hatj+3hatk|= sqrt(2^(2)+ (-6)^(2)+ 3^(2))` = 7 units
(b) Unit vector perpendicular to both `vecA & vecB`
`hatn = (vecAxx vecB)/(|vecAxx vecB|)= (2hati-6hatj+3hatk)/(7)`
`= (2)/(7)hati- (6)/(7)hatj+ (3)/(7) hatk`