Question

If a vector 2î + 3\[\hat j\] + 8\[\hat k\] is perpendicular to the vector 4\[\hat j\] - 4\[\hat i\] + m\[\hat k\], then the value of m is ______.

Options

• \[\frac {1}{2}\]

• -\[\frac {1}{2}\]

• 1

• -1

Answer 1

If a vector 2î + 3\[\hat j\] + 8\[\hat k\] is perpendicular to the vector 4\[\hat j\] - 4\[\hat i\] + m\[\hat k\], then the value of m is -\[\frac {1}{2}\].

Explanation:

Let \[\vec A\] = 2\[\hat i\] + 3\[\hat j\] + 8\[\hat k\] and \[\vec B\] = -4\[\hat i\] + 4\[\hat j\] + m\[\hat k\].

For \[\vec A\] perpendicular to \[\vec B\],

\[\vec A\] . \[\vec B\] = 0

\[\therefore\] (2\[\hat i\] + 3\[\hat j\] + 8\[\hat k\]) (-4\[\hat i\] + 4\[\hat j\] + m\[\hat k\]) = 0

\[\therefore\] -8 + 12 + 8m = 0

\[\therefore\] m = -\[\frac {1}{2}\]