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Find whether the lines vec(r)=(2hat(i)+3...

Find whether the lines `vec(r)=(2hat(i)+3hat(j)+hat(k))+t(5hat(j)-4hat(k))` and `vec(r)=(6hat(j)-hat(k))+s(hat(i)-3hat(j)+hat(k))`
intersect or not and if they inersect, find the position vector of their poin of intersection.

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The correct Answer is:
do not intersect
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Find the angle between the following pair of lines vec(r)=(3hat(i)+2hat(j)-4hat(k))+t(hat(i)+2hat(j)+2hat(k))" and "vec(r)=(hat(i)-2hat(j))+t'(3hat(i)+2hat(j)+6hat(k))

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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. Show that the lines (x-1)/(3)=(y+1)/(2)=(z-1)/(5) and (x+2)/(4)=(y-1)/...

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

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

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

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

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

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

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

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

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

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

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  14. Find the equation of the line passing through the points A(0,6,-9) and...

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  15. The shortest distance between the lines vec(r)=vec(a)+tvec(b) and vec(...

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  16. The shortest distance between the lines vec(r)=vec(a)(1)+tvec(b)(1) an...

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  17. The condition for intersecting the lines vec(r)=vec(a)(1)+tvec(b)(1) a...

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  18. The condition for collinearity for the two parallel lines vec(r)=vec(a...

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  19. The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(...

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  20. The shortest distance (in units) between the lines vec(r)=(hat(i)+2hat...

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