The distance of point 2,3,4 from the x-axis is k. The direction ratios of the line joining two points k+1,k−3,k , 1,−3,0 are

A
$(5, 5, 5)$
B
$(1, 1, 1)$
C
$(k^{2}, k^{2}, k^{2})$
D
$(2, 3, 4)$

Solution:

The length of the distance from the point $P (a, b, c)$ from $x -$ axis is $\sqrt{b^{2} + c^{2}}$

Hence, $k = \sqrt{3^{2} + 4^{2}} = 5$

The given points are $(6, 2, 5), (1, - 3, 0)$

The direction ratios of the line joining the points $A (x_{1}, y_{1}, z_{1})$ and $B (x_{1}, y_{1}, z_{1})$ is $〈x_{2} - x_{1}, y_{2} - y_{1}, z_{2} - z_{1}〉$

Therefore, the direction ratios of the line joining the points $(6, 2, 5), (1, - 3, 0)$ is $〈- 5, - 5, - 5〉 = 〈1, 1, 1〉$

The distance of point $(2, 3, 4)$ from the x-axis is $k$ . The direction ratios of the line joining two points $(k + 1, k - 3, k), (1, - 3, 0)$ are

Solution:

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