The angle between a line with direction ratios 2 , 2 , 1 and the line joining the points ( 3 , 1 , 4 ) and ( 7 , 2 , 12 ) is

Question

Aicharya · Accepted Answer

It is given that the direction ratios of first-line are $2, 2, 1$ and the direction ratios of second-line joining the points $(3, 1, 4)$ and $(7, 2, 12)$ are,

$(7 - 3, 2 - 1, 12 - 4)$

$(4, 1, 8)$

The angle between the two lines is,
$\cos θ = \frac{a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}}$

$\cos θ = \frac{2 \times 4 + 2 \times 1 + 1 \times 8}{\sqrt{9} \sqrt{81}} = \frac{18}{27}$

$θ = \cos^{- 1} (\frac{2}{3})$

The angle between a line with direction ratios 2 , 2 , 1 and the line joining the points ( 3 , 1 , 4 ) and (…

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