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Find the acute angle between the lines `(x-4)/(3)=(y+3)/(4)=(z+1)/(5) " and" (x-1)/(4)=(y+1)/(-3)=(z+10)/(5)` |
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Answer» Vector in the direction of first line `vecb=(hat3I+hat4j+hat5k)` Vector in the direction of second line `vec d=(hat4i-hat3j+hat5k)` Angle `theta` between two lines in given by `cos theta=(vecb.vecd)/(|vecb||vecd|)` `costheta =((hat3i+hat4j+hat5k).(4hati-3hatj+5hatk))/(|(hat3i+hat4j+5hatk)||(4hati-3hatj+5hatk)|)` `rArr cos theta =(12-12+25)/(sqrt(9+16+25)sqrt(9+16+25))` `rArr cos theta =(25)/(sqrt(50)sqrt(50))` `rArrcos theta =(1)/(2)` `rArrtheta= (pi)/(3)` |
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