Angle between the two planes of which one plane is $$4x+y+3z=0$$ and another plane containing the lines x−$$32=y$$−$$23=z$$−$$13$$,x−$$23=y$$−$$32=z$$−$$23$$ is

Question

Angle between the two planes of which one plane is $$4x+y+3z=0$$ and another plane  containing the lines x−$$32=y$$−$$23=z$$−$$13$$,x−$$23=y$$−$$32=z$$−$$23$$ is

Infinity Learn · Accepted Answer

Angle between the planes $$cos$$⁡θ$$=a1a2+b1b2+c1c2$$∑$$a12$$∑$$a22Equation$$ of the plane containing the lines ​x−$$32=y$$−$$23=z$$−$$13$$,x−$$23=y$$−$$32=z$$−$$23$$      is​                          x−$$3y$$−$$2z$$−$$1233323=0$$​⇒$$3x$$−$$3+3y$$−$$2$$−$$5z$$−$$1=0$$​⇒$$3x+3y$$−$$5z$$−$$10=0$$​∴$$cos$$θ$$=12+3$$−$$152222=0$$⇒θ$$=$$π$$2$$

$Angle between the two planes of which one plane is 4 x + y + 3 z = 0 and another plane$
$containing the lines \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{3}, \frac{x - 2}{3} = \frac{y - 3}{2} = \frac{z - 2}{3} is$

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Angle between the two planes of which one plane is 4x+y+3z=0 and another plane containing the lines x−32=y−23=z−13,x−23=y−32=z−23 is

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$Angle between the two planes of which one plane is 4 x + y + 3 z = 0 and another plane$
$containing the lines \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{3}, \frac{x - 2}{3} = \frac{y - 3}{2} = \frac{z - 2}{3} is$