First slide

Introduction to 3-D Geometry

Question

If the dr’s of a line are $(1 + λ, 1 - λ, 2)$ and it makes an angle $60^{0}$ with the Y- axis then $λ$ is

Moderate

A

$1 \pm \sqrt{3}$
B

$4 \pm \sqrt{5}$
C

$2 \pm 2 \sqrt{5}$
D

$2 \pm \sqrt{5}$

Solution

$\cos β = \frac{b}{\sqrt{a^{2} + b^{2} + c^{2}}} (a_{1}, b_{1}, c_{1}) = (1 + λ, 1 - λ, 2) (a_{2}, b_{2}, c_{2}) = (0, 1, 0)$
$\Rightarrow λ^{2} - 4 λ - 1 = 0 \Rightarrow λ = 2 \pm \sqrt{5}$

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