Question

A and B are two vectors given by A=-i+3j+2k amd B=i+j. then a vector pf magnitude 3 which is perpendicular to both A and B.?​

Answer 1

let the required vector is "C".

so, C = magnitude × direction

magnitude = 3

direction = unit vector perpendicular to both A and B.

= unit vector of (A × B)

= (A × B) / |A × B|

A × B = i (0 - 2 ) + j ( 2 - 0 ) + k ( -1 - 3 )

= -2 i + 2 j - 4 k

| A × B | = √( 4 + 4 + 8 ) = √16 = 4

hence,

C = 3 (A × B) / |A × B|

C = 3 × 2( -i + j -2k) / 4

C = (3/2) ( -i + j + 2k)....... answer.

or, C = (3/2) ( i - j - 2k)....... answer.

answer...