Question

15. (a) Five forces acting on a particle are represented by (2i+3j), (4i-7j), (-5i+8j), (i+j) and (pi+qj), where p,q∈R. If the particle is in equilibrium, find the values of p and q.
(b) WXYZ is a parallelogram whose vertices are W(-1,1), X(m,n), Y(5,-7) and Z(2,4). Find: (i) values of m and n; (ii) the unit vector in the direction of XY.

Accepted Answer

(a) For equilibrium, the sum of all forces must be zero. Adding the i and j components: (2+4-5+1+p)=0 gives p=-2; (3-7+8+1+q)=0 gives q=-5.
(b)(i) In a parallelogram WXYZ, diagonals WY and XZ bisect each other, so their midpoints are equal. Midpoint of WY = (2,-3). Setting midpoint of XZ = (2,-3): (m+2)/2=2 gives m=2; (n+4)/2=-3 gives n=-10.
(ii) X=(2,-10), Y=(5,-7). XY = Y-X = (3,3), |XY|=√18=3√2. Unit vector = (1/3√2)(3,3) = (√2/2, √2/2), i.e. (√2/2)i + (√2/2)j.

WAEC Further Mathematics 2025 Theory — Question 15

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