Find the angle between two lines, one of which was direction ratios 2, 2, 1 while the other one is obtained by joining het points (3, 1, 4) and (7, 2, 12).

Explanation

It is Given that,

Direction ratios of first line are 2,2,1

Direction ratios of second line joining the points (3,1,4)(7,2,12) and (7 -
3),(2-1),(12-4)

i.e 4,1,8

Let `theta` be the angle between the two lines.


`therefore cos theta=frac{2(4)+2(1)+1(8)}{sqrt{(2)^{2}+(2)^{2}+(1)^{2}} sqrt{(4)^{2}+(1)^{2}+8^{2}}} `

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