If the projections of a line of length d on the coordinate axes are d1,d2, d3 respectively, thend12+d22+ d32−d2=

If the projections of a line of length $d$ on the coordinate axes are $d_{1}, d_{2}, d_{3}$ respectively, then ${d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2} - d^{2} =$

A
$d^{2}$
B
1
C
0
D
None

Solution:

If $d_{1}, d_{2}, d_{3}$ are the projections of a line segment of length $d$ on the coordinate axes then $d^{2} = {d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2}$

Therefore, ${d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2} - d^{2} = 0$

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