Let a =3 i - j + k and b = i + j +3 k . If the area of the parallelogram whose adjacent sides are represented by the vectors a and b , is 8 3 sq. units, then a b is equal to

Step-by-step solution

aligned a b & = | array ccc i & j & k 3 & - & 1 1 & & 3 array | & =-4 i -8 j +4 k aligned Area of parallelogram =| a b | aligned & 8 3 = 16 ^2+64+16 ^2 & 8 3 = 32 ^2+64 aligned Squaring on both sides, we get aligned & 192=32 ^2+64 & 32 ^2=128 & ^2=4 & aligned & a ~b =(3 i - j + k ) ( i + j +3 k ) & =3- ^2+3 & =6-4 & =2 aligned aligned