Question

If the projections of the line segment $AB$ on the coordinate axes are $12,3,k$ and $AB=13$, then $k^2-2k+3$ is equal to:

• A. $0$
• B. $1$
• C. $11$
• D. $27$

Answer 1

Answer: (C), (D)

The correct options are
C $11$
D $27$

Let a,b,c be the projection of a line on the coordinate axes.

Then the length of the line given by $\sqrt{a^2+b^2+c^2}$.

Here we have ${12}^2+3^2+k^2=169$

$\Rightarrow k=\pm 4$.

Thus $k^2-2k+3=11$ or $27$.