InterviewSolution
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InterviewSolution
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If p be the length of the perpendicular from the origin on the straight line `ax+by=p` and `b=sqrt(3)/2`, then what is the angle between the perpendicular and the positive direction of x-axis ?A. `30^(@)`B. `45^(@)`C. `60^(@)`D. `90^(@)` |
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Answer» Correct Answer - C Equation of line is `ax+by-p=0`, then length of perpendicular, from the origin. `p=|(axx0+bxx0-p)/sqrt(a^(2)+b^(2))| or p=|(-p)/sqrt(a^(2)+b^(2))|` or `|1/sqrt(a^(2)+b^(2))|=1 or a^(2)+b^(2)=1` `b=sqrt(3)/2 or b^(2)=3/4` `a^(2)+3/4=1` `a^(2)=1/4 implies a=1/2 " "[a=-1/2" not taken since angle is with +ve direction to x-axis."]` Equation is `1/2 x+sqrt(3)/2 y=p` or `x cos 60^(@)+y sin 60^(@)=p` Angle `=60^(@)` |
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