Question

For vectors \[\vec P\] = 4î - ĵ + 8k̂ and \[\vec Q\] = 2î - mĵ + 4k̂ to have the same direction, what is the value of m?

Options

• \[\frac {1}{2}\]

• 2

• \[\frac {1}{4}\]

• 4

Answer 1

\[\frac {1}{2}\]

Explanation:

For vectors to have the same direction, their components must be proportional: \[\frac {P_x}{Q_x}\] = \[\frac {P_y}{Q_y}\]. So \[\frac {4}{2}\] = \[\frac {-1}{-m}\], which gives 2 = \[\frac {1}{m}\], therefore m = \[\frac {1}{m}\].