Question

The unit vector parallel to the resultant of the vectors \[\vec A\] = 4\[\hat i\] + 3\[\hat j\] + 6\[\hat k\] and \[\vec B\] = -\[\hat i\] + 3\[\hat j\] - 8\[\hat k\] is ______.

Options

• \[\frac {1}{7}\](3\[\hat i\] + 6\[\hat j\] - 2\[\hat k\])

• \[\frac {1}{7}\](3\[\hat i\] + 6\[\hat j\] + 2\[\hat k\])

• \[\frac {1}{49}\](3\[\hat i\] + 6\[\hat j\] - 2\[\hat k\])

• \[\frac {1}{49}\](3\[\hat i\] - 6\[\hat j\] + 2\[\hat k\])

Answer 1

The unit vector parallel to the resultant of the vectors \[\vec A\] = 4\[\hat i\] + 3\[\hat j\] + 6\[\hat k\] and \[\vec B\] = -\[\hat i\] + 3\[\hat j\] - 8\[\hat k\] is \[\frac {1}{7}\](3\[\hat i\] + 6\[\hat j\] - 2\[\hat k\]).

Explanation:

The unit vector parallel to the resultant is obtained by dividing the resultant vector by its magnitude, giving \[\frac {1}{7}\](3\[\hat i\] + 6\[\hat j\] - 2\[\hat k\]).