Statics/Physics/ Mathematics?

Question

1) Find the position vector from B to A, rBA ? { i + j + k} m

2) find the position vector from B to C, rBC ? { i + j + k} m

3) Find the result of inner product (rBA·rBC)m?

4) Find the distance between B and A ? m

5) Find the distance between B and C ? m

6) Find the angle, θ ? °

7) Find position vector from C to B, rCB ? { i + j + k} m

8) Find the force vector F along CD, FCD ? { i + j + k} N

9) Find the force component of F along CB, FCB ? { i + j + k} N

NCS · Accepted Answer

I'll use (x, y, z) notation instead of "x i + y j + z k" -- I think it's cleaner.

1) rBA = (0, -2, 0) m

2) rBC = (3, 5, -1) m

3) rBA•rBC = (0*3 - 2*5 - 0*1) m² = -10 m²

4) dBA = 2 m

5) dBC = √(3² + 5² + 1²) m = √35 m ≈ 5.9 m

6) cosΘ = a•b / |a|*|b| = -10 / 2*√35 = -0.845
Θ = 148º

7) rCB = -rBC = (-3, -5, 1) m

8) It looks like F = 30N*(5, -5, 1)/√(5²+5²+1²)
and so F = (21, -21, 4.2) N

9) FCB = F•rCB / |rCB| = (21, -21, 1)N•(-3, -5, 1)m/√(3²+5²+1²)m
FCB = (21*-3 + 21*5 + 1*1)N·m / √35m = 7.3 N

But check the math.

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