If $θ$ is the angle between the lines whose DR's are $(1, - 2, 1), (4, 3, 2),$ then $sec \frac{θ}{2} + cosec \frac{θ}{2} =$

2 \sqrt{2}

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\sqrt{2}

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\frac{1}{2 \sqrt{2}}

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Solution

The correct option is A $2 \sqrt{2}$
Given: DR's $(1, - 2, 1), (4, 3, 2)$
i.e. $(1, - 2, 1) = (a_{1}, b_{1}, c_{1})$ and
$(4, 3, 2) = (a_{2}, b_{2}, c_{2})$
For angle $θ$ Finding value of
$\Rightarrow a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}$
$\Rightarrow 1 \times 4 + (- 2) \times 3 + 1 \times 2$
$\Rightarrow 4 - 6 + 2$
$\Rightarrow 0$
Since, $a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$ Hence, $θ = \frac{π}{2}$
Now finding, $sec \frac{θ}{2} + cosec \frac{θ}{2} = sec \frac{π}{4} + cosec \frac{π}{4} = \sqrt{2} + \sqrt{2}$
$\Rightarrow sec \frac{θ}{2} + cosec \frac{θ}{2} = 2 \sqrt{2}$

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