A particle, P, is moving with constant velocity 8i − 12j A second particle, Q, is moving with constant velocity αi + 9j Q travels in a direction which is parallel to the motion of P - AQA - A-Level Maths Pure - Question 12 - 2020 - Paper 2

To find the value of α, we need to determine the conditions for the velocities of particles P and Q to be parallel.

The velocity of particle P is given by: $extbf{v}_P = 8 extbf{i} - 12 extbf{j}$

The velocity of particle Q is given by: extbf{v}_Q = oldsymbol{α extbf{i}} + 9 extbf{j}

For two vectors to be parallel, one must be a scalar multiple of the other. Hence, we can express this relationship as:

rac{8}{α} = rac{-12}{9}

Cross-multiplying gives:

$8 imes 9 = -12 imes α$

This simplifies to:

$72 = -12α$

Now, divide both sides by -12:

$α = -6$

Thus, the value of α is -6.