The equation of motion of a point in space is x = 2 t , y = − 4 t , z = 4 t , where t is measured in hours and the coordinates of the moving point in kilometres. The distance of the point from the sta

Question

The equation of motion of a point in space is x = 2 t , y = − 4 t , z = 4 t , where t is measured in hours and the coordinates of the moving point in kilometres. The distance of the point from the starting point O ( 0 , 0 , 0 ) in 10 hours is

TestHub · Accepted Answer

Eliminating t , the path is 2 x ​ = − 4 y ​ = 4 z ​ , a straight line through the origin. For t = 10 : x = 20 , y = − 40 , z = 40 and ∣ OM ∣ = 400 + 1600 + 1600 ​ = 60 km .

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