First slide

Direction ratios and direction cosines

Question

The base of the pyramid AOBC is an equilateral triangle OBC with each side is equal to $4 \sqrt{2}$ . ‘O’ being the origin of reference, AO is perpendicular to the plane of triangle OBC and AO = 2. Then the cosine of the angle between the skew lines one passes through A and midpoint of OB, and the other passing through O and the mid point of BC can be

Moderate

A

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

0
C

$\frac{1}{\sqrt{6}}$
D

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

Solution

Take OB as X-axis. we have $B = (4 \sqrt{2}, 0, 0)$ ,
$A = (0, 0, 2) a n d C = (2 \sqrt{2}, 2 \sqrt{6}, 0)$ .
Mid point of OB is $(2 \sqrt{2}, 0, 0)$ , Mid point of BC is $(3 \sqrt{2}, \sqrt{6}, 0)$ , hence the direction ratios of the lines be $2 \sqrt{2} : 0 : - 2$ and $3 \sqrt{2} : \sqrt{10} : 0$

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