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Determine whether the following pair of lines intersect or not :
(i) `vec(r)=(hat(i)-hat(j)+hat(k))+t(2hat(i)+hat(k)),vec(r)=(2hat(i)-hat(j)-hat(k))+s(2hat(i)+3hat(k))`
(ii) `(x-1)/(3)=(1-y)/(1)=(z+2)/(0)" and "(x-4)/(2)=(y-0)/(0)=(z+1)/(3)`
(iii) `(x-5)/(4)=(y-7)/(4)=(z+3)/(-5)" and "(x-3)/(7)=(y-4)/(1)=(z-5)/(3)`

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The correct Answer is:
(i) intersect (ii) do not intersect (iii) intersect
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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
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  3. Determine whether the following pair of lines intersect or not : (i)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Find the shortest distance between the two lines whose vector equation...

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