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Find the equation of the line which passes through the point with position vector `-hat(i)+2hat(j)+hat(k)` and which is at right angles to each of the lines : `(2x-1)/(4)=(3y+5)/(2)=(2-z)/(3)" and "(x)/(-3)=(y)/(2)=(z)/(5)`

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The correct Answer is:
`(-hat(i)+2hat(j)+hat(k))+t((28)/(3)hat(i)-hat(j)+6hat(k))`
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Find the equation of the line which passes through the point with position vector -hati + 2hat j + hat k and which is at right angles to each of the lines: (2x -1)/4 = (3 y + 5)/2 =(2 - z)/3 and x/-3 = y/2 = z/3 .

Find the vector equation of a line which passes through the point with position vector hat(i)-2hat(j)+4hat(k) and is in the direction of hat(i)+2hat(j)-hat(k) . Also, reduce it to cartesian from.

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the equation of the line passing through the point (2,-1,3) and parallel to the line vec(r)=(hat(i)-2hat(j)+hat(k))+lamda(2hat(i)+3hat(j)-5hat(k))

Find the equation in vector form of a line which is parallel to the vector hat(i)-2hat(j)+3hat(k) and which passes through the point (1,-2,5). Reduce it to cartesian form.

Find the equation of a plane through the intersection of the planes vecr.(hati+3hat j-hat k)=5 and vecr.(2hat i-hatj +hatk)=3 and passing through the point (2,1,-2)

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

Find the point where line which passes through point (1,2,3) and is parallel to line vec r= hat i+ hat j+2 hat k+lambda( hat i-2 hat j+3 hat k) meets the xy-plane.

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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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. Find the angle between the pair of lines with direction ratios given ...

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  2. Find the equation of the line passing through the point (1,2,3), which...

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  3. Find the equation of the line which passes through the point with posi...

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  4. If the lines (x-1)/(-3)=(y-2)/(2lamda)=(z-3)/(2)" and "(x-1)/(3lamda)=...

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  5. Slow that the lines (x-5)/(7)=(y+2)/(-5)=(z)/(1) and (x)/(1)=(y)/(2)=(...

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  6. If the coordinates of the points A,B,C,D be (1,2,3), (4,5,7), (-4,3,-6...

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  7. Show that the lines (x+1)/(3)=(y+3)/(5)=(z+5)/(7) and x-2=(y-4)/(3)=(z...

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  8. Show that the lines (x-1)/(3)=(y+1)/(2)=(z-1)/(5) and (x+2)/(4)=(y-1)/...

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  9. Show that the line through P(3,9,4) and Q(-4,4,4)) intersect the line ...

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  10. Find whether the lines vec(r)=(2hat(i)+3hat(j)+hat(k))+t(5hat(j)-4hat(...

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  11. Determine whether the following pair of lines intersect or not : (i)...

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  12. The perpendicular distance of the points (1,0,0) from the y-axis is -

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  13. The perpendicular distance of the point (1,1,0) from the z-axis is -

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  14. The perpendicula distance of the points (1,1,1) from the x-axis is -

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  15. The perpendicular distance of the point (1,2,3) from the x-axis is -

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  16. Find the distance of the point (1,0,0) from the line (x-1)/(2)=(y+1)/(...

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  17. A(1,0,4), B(0,-11,3), C(2,-3,1) are three points and D is the foot of ...

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  18. Find the length of the perpendicular drawn from the point (5,4,-1) to ...

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  19. Let l(1),m(1),n(1),l(2),m(2),n(2)" and "l(3),m(3),n(3) be the durectio...

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  20. Find the equation of the perpendicular drawn from the point P(-1,3,2) ...

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