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The cartesian equations of a line are 3x...

The cartesian equations of a line are `3x+1=6y-2=1-z`. Find the fxed point through which it passes, its direction ratios and also its vector equation.

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The correct Answer is:
`(-(1)/(3),(1)/(3),1);2,1,-6;(x+(1)/(3))/(2)=(y-(1)/(3))/(1)=(z-1)/(-6);`
`vec(r)=(-(1)/(3)hat(i)+(1)/(3)hat(j)+hat(k))+t(2hat(i)+hat(j)-6hat(k))`
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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. The cartesian equation of a line is (x+3)/(2)=(y-5)/(4)=(z+6)/(2). the...

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  2. The cartesian equation of a line is 3x+2=5y-4=3-z. Find a point on t...

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  3. The cartesian equations of a line are 3x+1=6y-2=1-z. Find the fxed poi...

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  4. Find the equation of the line which passes through (1,2,-4) and (4,-5,...

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  5. The equation of a line is given by x=by+c, z=ay+d, write it in cartes...

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  6. Let the position vectors of the points P, Q and R are respectively giv...

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  7. Show that the poins whose position vectors are 4hat(i)+5hat(k),hat(i)+...

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  8. Find the points on the line (x+2)/(3)=(y+1)/(2)=(z-3)/(2) at a distanc...

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  9. Show that the line joining the points P and Q with position vectors ve...

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  10. (i) Find the vector equation of a line passing through a point with po...

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  11. The angle between the straight lines (x-4)/(2)=(y-5)/(0)=(z-6)/(0) and...

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  12. The angle between the straight lines x=5,y=4t+5,z=4t+3 and (x-5)/(5)=(...

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  13. The straight lines (x-x(1))/(l(1))=(y-y(1))/(m(1))=(z-z(1))/(n(1))" an...

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  14. The straight lines (x)/(a(1))=(y)/(b(1))=(z)/(c(1)) and (x-2)/(a(2))=(...

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  15. State which of the following statement is true ?

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  16. The angles between the lines (x-5)/(2)=(y-3)/(2)=(z)/(0) and x=5,y=8,z...

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  17. The angle between the lines(x-5)/(1)=(y-1)/(0)=(z-9)/(0) and 2x-1=5-2y...

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  18. The lines (x)/(1)=(y)/(2)=(z)/(3) and (x-1)/(-2)=(y-2)/(-4)=(3-z)/(6) ...

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  19. Find the angle between the lines (x-5)/(7)=(y+2)/(-5)=(z-9)/(1) and (x...

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  20. Find the angle between the lines (x-7)/(2)=(y-6)/(3)=(z+2)/(-4) and (2...

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