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BACK 發問時間: 科學數學 · 1 0 年前

Dot Product問題

1. A tow truck drags a stalled car along a road. The chain makes an angle of 30 degrees with the road and the tension in the chain is 1500N. How much work is done by the truck in pulling the car 1 km?

2. Find the angle between a diagonal of a cube and a diagonal of one of its faces.


1 個解答

  • 1 0 年前

    1. W=F(dot product) D, with | F|=1500N, |D|=10^3m, and the angle between F and D is 30 degree. So Work W= sqrt(3)/2*(1.5)*10^6 Nm (牛頓米)= sqrt(3)/2*(1.5)*10^6 J (焦耳) .

    2. Orient the cube on a 3-D coordinate system so that A(0,0,0), B(1,1,0), and C(1,1,1) are 3 vertices of the cube. Also we notice that AB is a diadonal of a face; and AC is a diagonal. Therefore the problem is to find the angle (theta) between AC abd AB. Use dot porduct : cos (theta)= (AB dot AC)/[|AB|*|AC|] = sqrt(2/3) or theta = arccosine (sqrt(2/3)) . In the above I have used 1 as a side of the cube. The angle theta will be the same if other size of the cube are considered.

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