The cantilever beam depicted below is rigidly attached to a wall at point A, which coincides with the coordinate system's origin. Point B near the beam's free end has coordinates (1.3, 0.3, 2.4) m. The vector ☎₁ = lî+12ĵ+1k m is perpendicular to the beam axis AB and oriented parallel to the width dimension of the cross-section, as shown. The vector 7₂ = 29.1î+1.2ĵ — 14.7k m is perpendicular to the beam axis AB and r₁. The force ℗ applied to point B of the beam has the direction angles 0º = 144°,0y = 72°,0₂ = 60°. 12 Questions: a Assuming |P| = 1000 N Compute the force moment about rị and 72. b Previous experiments on similar beams made of the same material have shown that the beam will rupture and be torn from the wall when the absolute value of the moment of P about r₁ is 4000 Nm, or when the absolute value of the moment of P about r2 is 6000 Nm. Determine the magnitude of P that will cause this beam to fail.

Given:

The coordinates of point A, A(0,0,0)

The coordinates of point B, B (1.3,0.3,2.4) m

The position vector, r₁ = I + 12j +k

The position vector, r₂ = 29.1i + 1.2j – 14.7k

The angle, θ_x = 144ᵒ

The angle, θ_y = 72ᵒ

The angle, θ_z = 60ᵒ

The magnitude of force, P = 1000 N