Write the angle between the lines whose direction ratios are proportional to 1, -2, 1 and 4, 3, 2.

Explanation

The direction ratios of the first line are `1,-2,1` and the direction ratios of the second line are `4,3,2`.


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


Now ,


``
`cos theta=|frac{1(4)+(-2)(3)+1(2)}{sqrt{(1)^{2}+(-2)^{2}+(1)^{2}} sqrt{(4)^{2}+(3)^{2}+(2)^{2}}}|`


`=|frac{4-6+2}{sqrt{1+4+1} sqrt{16+9+4}}|`


`=frac{0}{sqrt{6} sqrt{29}}`


`=0`


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