Let A→ = (150iˆ+270jˆ) mm, B→ = (300iˆ-450jˆ) mm, and C→ = (-100iˆ-250jˆ) mm. Find scalars r and s, if possible, such that R→=rA→+sB→+C→ has zero x and y components.

Answer: r = 0.8081; s = - 0.07071

Explanation:

A = (150i + 270j) mm

B = (300i - 450j) mm

C = (-100i - 250j) mm

R = rA + sB + C = 0i + 0j

R = r (150i + 270j) + s (300i - 450j) + (-100i - 250j) = 0i + 0j

R = (150r + 300s - 100) i + (270r - 450s - 250) j = 0i + 0j

Equating the i and j components;

150r + 300s - 100 = 0

270r - 450s - 250 = 0

150r + 300s = 100

270r - 450s = 250

solving simultaneously,

r = 0.8081 and s = - 0.07071

QED!