1.

Consider a three dimensional Cartesian system with origin at O and three rectangular coordinate axes x,y and z-axis. Suppose that the distance between two points P and Q in the space having their coordinates (x _(1), y_(1), z _(1)) and (x _(2), y _(2), z _(2)) respectively be defined by the following formula d (P,Q) =|x_(2)-x_(1)|+ |y_(2)-y_(1)|+ |z _(2) -z_(1)| Although the rormula of distance between two points has been defined in a new way, yet the other definition remain same (like section formula, direction consines ets). So, in general equations of straight line in space, plane in spece remain unchanged. If l, m, n represent direction consines (if we can call it) of a vactor bar(OP), then which of the following relations holds?

Answer»

`L ^(2) + m ^(2) + N ^(2) =1`
`l+m+n =1`
`| l + m+ n|=1`
`|l| + |m| + |n| =1`

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