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# Find the angle between the following pairs of lines :

and

Answer :

In the Cartesian or symmetrical form of equation the angle between two lines can be found by dot product equation and in this equation we will use the direction ratios which are in the denominator of the equation. in this equation a,b,c are the direction ratios of this equation.

Equations of the given lines are,

and

a_{1} = 3, b_{1} = 5, c_{1} = 4 ; a_{2} = 1, b_{2} = 1, c_{2} = 2

now to find the angle between two lines we use cross product equation,

cos θ =

cos θ =

cos θ =

θ =

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