Question

For \[\vec b_1=2\hat i-\hat j+\hat k\] and \[\vec b_2=3\hat i-5\hat j+2\hat k\], what is \[\vec b_1\times\vec b_2\]?

Options

• \[-3\hat i+\hat j+7\hat k\]

• \[3\hat i+\hat j-7\hat k\]

• \[10\hat i-6\hat j+3\hat k\]

• \[3\hat i-\hat j-7\hat k\]

Answer 1

Evaluating the determinant with rows \[(2,-1,1)\] and \[(3,-5,2)\] gives \[3\hat i-\hat j-7\hat k\]. This vector is perpendicular to both \[\vec b_1\] and \[\vec b_2\].