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Given P = 4i – j + 8k and Q = 2i – mj + 4k find m if  P and Q have the same direction.

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Since P and Q have the same direction, their corresponding components must be in the same proportion, i.e.,

\(\frac{P_x}{Q_x}=\frac{P_y}{Q_y}=\frac{P_z}{Q_z}\)

\(\frac{4}{2}=\frac{-1}{-m}=\frac{8}{4}\)

\(\therefore \,m=\frac{1}{2}\)

Value of m is \(\frac{1}{2}\).

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