First slide

Direction ratios and direction cosines

Question

If $θ$ is the angle between two lines whose d.r’s are (1,-2,1) and (4,3,2) then $\sec (\frac{θ}{2}) + \cos e c (\frac{θ}{2}) =$

Moderate

A

$\sqrt{2}$
B

$\infty$
C

$2 \sqrt{2}$
D

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

Solution

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$ $\Rightarrow θ = 90^{o}$
$∴ \sec \frac{θ}{2} + \cos e c \frac{θ}{2} = \sqrt{2} + \sqrt{2} = 2 \sqrt{2}$

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