First slide

Direction ratios and direction cosines

Question

The number of lines which are equally inclined to the coordinate axes, is k. If $k^{2} + e^{\log_{e^{6}} {(A + 1)}^{3}} (k) = 4 k$ . Then $k - A =$

Easy

A

4
B

5
C

6
D

3

Solution

The number of lines which are equally inclined to the coordinate axes is 4
Hence, substitute $k = 4$ in the equation $k^{2} + e^{\log_{e^{6}} {(A + 1)}^{3}} (k) = 4 k$
$\begin{matrix} 16 + 4 \sqrt{A + 1} = 16 \\ A = - 1 \end{matrix}$
Therefore, $k - A = 4 + 1 = 5$

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