Let ( m ) be a vector of magnitude ( 3 ) and perpendicular to the vectors ( i + j ) and ( j - k ). Let ( n ) be another vector of magnitude (2 6 ) and perpendicular to the vectors (2 i - j ) and ( j +2 k ). The area (in sq. units) of the triangle formed with ( m ) and ( n ) as sides is

Step-by-step solution

Given, ( m = 3 unit vectors of [( i + j ) ( j - k )] ) ( aligned ( i + j ) ( j - k ) & = [ array ccc i & j & k 1 & 1 & 0 0 & 1 & -1 array ] & = i (-1-0)- j (-1-0)+ k ( l ) & =- i + j + k m & = 3 - i + j + k 1+1+1 & = 3 - i + j + k 3 =- i + j + k aligned ) and ( n =2 6 ) unit vectors of ([(2 i - j ) ( j +2 k )] ) ( aligned & (2 i - j ) ( j +2 k ) &= [ array ccc i & j & k 2 & -1 & 0 0 & 1 & 2 array ] &= i (-2-0)- j (4-0)+ k (2+0)=-2 i -4 j +2 k & n =2 6 -2 i -4 j +2 k 4+16+4 =2 6 -2 i -4 j +2 k 2 6 aligned ) (=-2 i -