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Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector `3hat(i)+2hat(j)-8hat(k)`.

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The correct Answer is:
`vec(r)=(5hat(i)+2hat(j)-4hat(k))+t(3hat(i)+2hat(j)-8hat(k));(x-5)/(3)=(y-2)/(2)=(z+4)/(-8)`
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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. Write the vector equation of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2).

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  2. Find the equation in vector form of a line which is parallel to the ve...

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  3. Find the vector and cartesian equations of the line through the point ...

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  4. The cartesian equation of a line is (x+3)/(2)=(y-5)/(4)=(z+6)/(2). the...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. State which of the following statement is true ?

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

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

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