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If the projections of the line segment $\bar{A B}$ on the coordinate planes are $2, k, 6$ and $A B = 6$ , then $\sqrt{k^{2} - 7} =$

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Correct option is C

If d1,d2,d3 are the projections of the line segment of length don the coordinate planes thend12+d22+d32=2d2 ⇒22+k2+62=262⇒4+36+k2=72⇒k2=32Therefore,k2−7=5

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If the projections of the line segment AB¯ on the coordinate planes are 2,k,6 and AB=6, thenk2−7=

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If the projections of the line segment $\bar{A B}$ on the coordinate planes are $2, k, 6$ and $A B = 6$ , then $\sqrt{k^{2} - 7} =$