The direction ratios of the diagonal of a cub | vedclass

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(B) Let the side length of the cube be $a$.Since the $3$ concurrent edges are along the coordinate axes,the origin is at $(0, 0, 0)$ and the opposite

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$1, 1, 1$

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(B) Let the side length of the cube be $a$.Since the $3$ concurrent edges are along the coordinate axes,the origin is at $(0, 0, 0)$ and the opposite corner is at $(a, a, a)$.The direction ratios of the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are given by $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.Substituting the coordinates,we get $(a - 0, a - 0, a - 0) = (a, a, a)$.Since direction ratios are proportional,we can divide by $a$ to get $(1, 1, 1)$.Thus,the direction ratios are $1, 1, 1$.

The direction ratios of the diagonal of a cube that joins the origin to the opposite corner are (when the $3$ concurrent edges of the cube are the coordinate axes):

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