A particle, P, is moving with constant velocity 8i − 12j - AQA - A-Level Maths Mechanics - Question 12 - 2020 - Paper 2

To find the value of α such that the velocity of particle Q is parallel to that of particle P, we first note the velocity vector of P, which is given as:

$ext{Velocity of } P = 8i - 12j$

The direction vector for Q, which must be parallel to that of P, is:

$ext{Velocity of } Q = αi + 9j$

For two vectors to be parallel, they must be scalar multiples of each other. Therefore, we can set up the following ratio:

$\frac{α}{8} = \frac{9}{-12}$

Cross-multiplying gives:

$α \times -12 = 8 \times 9$

This simplifies to:

$-12α = 72$

Solving for α:

$α = \frac{72}{-12} = -6$

Thus, the value of α is ( -6 ).