Question

Determine the vector product of `vec"v"_1 = 2hat"i" + 3hat"j" - hat"k" and vec"v"_2 = hat"i" + 2hat"j" - 3hat"k"`

Answer 1

As `vec"A" xx vec"B" = |(hat"i",hat"j",hat"k"),("A"_"x","A"_"y","A"_"z"),("B"_"x","B"_"y","B"_"z")|`

Using determinant to find vector product,

∴ `vec"v"_1 xx vec"v"_2 = |(hat"i",hat"j",hat"k"),(2,3,-1),(1,2,-3)|`

`= [(3xx-3)-(-1xx2)]hat"i" + [(-1xx1) - (2xx-3)]hat"j" + [(2xx2) - (3xx1)]hat"k"`

`= [-9 + 2]hat"i" + [-1 + 6]hat"j" + [4 - 3]hat"k"`

`= -7hat"i" + 5hat"j" + hat"k"`

Required vector product is `-7hat"i" + 5hat"j" + hat"k"`