The straight line \; x-3/3 = \; y-2/1 = \; z-1/0 is

Correct Answer is : perpendicular to the zzz-axis.

Correct Answer is : perpendicular to the zzz-axis.

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WBJEE 2025 Math Paper

Question : 45 of 75

Marks: +1, -0

\; \frac{x-3}{3} = \; \frac{y-2}{1} = \; \frac{z-1}{0}

Solution:

Symmetric form

\; \frac{x-3}{3} = \; \frac{y-2}{1} = \; \frac{z-1}{0} = t

Equivalently,

(x, y, z) = (3, 2, 1) + t(3, 1, 0)

So its direction vector is

d = (3, 1, 0).

Compare with the

z

-axis direction vector

k = (0, 0, 1)

d \cdot k = 3 \cdot 0 + 1 \cdot 0 + 0 \cdot 1 = 0

A zero dot product means the two lines are perpendicular.

Since it's neither purely along

x

nor

y

, but its direction is orthogonal to the

z

-axis, the correct choice is

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