Ex 10.4, 2

Transcript

Ex 10.4, 2 Find a unit vector perpendicular to each of the vector + and , where = 3 + 2 + 2 and = + 2 2 . = 3 + 2 + 2 = 1 + 2 2 ( + ) = (3 + 1) + (2 + 2) + (2 2) = 4 + 4 + 0 ( ) = (3 1) + (2 2) + (2 ( 2)) = 2 + 0 + 4 Now, we need to find a vector perpendicular to both + and , We know that ( ) is perpendicular to and Replacing by ( + ) & by ( ) ( + ) ( ) will be perpendicular to ( + ) and ( ) Let = ( + ) ( ) = 4 2 4 0 0 4 = 4 4 (0 0) 4 4 (2 0) + 4 0 (2 4) = (16 0) (16 0) + (0 8) = 16 16 8 = 16 16 8 Now, Unit vector of = 1 Magnitude of = 162+ 16 2+ 8 2 = 256+256+64 = 576 = 24 Unit vector of = 1 = 1 24 16 16 8 = . Therefore the required unit vector is 2 3 2 3 1 3 . Note: There are always two perpendicular vectors So, another vector would be = = + + Hence, the perpendicular vectors are 2 3 2 3 1 3 & 2 3 + 2 3 + 1 3