Question

For the parallel lines with \[\vec a_2-\vec a_1=2\hat i+\hat j-\hat k\] and \[\vec b=2\hat i+3\hat j+6\hat k\], what is \[\vec b\times(\vec a_2-\vec a_1)\]?

Options

• \[9\hat i-14\hat j+4\hat k\]

• \[4\hat i-14\hat j+9\hat k\]

• \[-9\hat i+14\hat j-4\hat k\]

• \[2\hat i+4\hat j+5\hat k\]

Answer 1

The cross product is evaluated using the components \[(2,3,6)\] and \[(2,1,-1)\]. It gives \[-9\hat i+14\hat j-4\hat k\], whose magnitude is \[\sqrt{293}\].