JEE Main · 2007 · 29 Apr 2007 · Offline · Three Dimensional Geometry

If a line makes an angle of

\frac{π}{4}

with the positive directions of each of

x

-axis and

y

-axis, then the angle that the line makes with the positive direction of the

z

-axis is

(A) $\frac{π}{6}$
(B) $\frac{π}{3}$
(C) $\frac{π}{4}$
(D) $\frac{π}{2}$ ✓ Correct

Answer: (D)

Solution

The direction cosines of a line satisfy

l^{2} + m^{2} + n^{2} = 1

. With the line at

\frac{π}{4}

to both the

x

- and

y

-axes,

l = m = \frac{1}{2}

, so

\frac{1}{2} + \frac{1}{2} + n^{2} = 1

forces

n = 0

. Since

n = cos γ

, the line makes an angle

γ = \frac{π}{2}

with the

z

-axis.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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