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Consider the lines (x-5)/(3)=(y-7)/(-16)...

Consider the lines `(x-5)/(3)=(y-7)/(-16)=(z-3)/(7)` and `(x-9)/(3)=(y-13)/(8)=(z-15)/(-5)` , then-

A

the two lines intersect

B

the two lines are skew

C

the shortest distance between the lines is 14

D

direction numbers of the line of shortest distance are 2,3,6

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The correct Answer is:
B, C, D
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Find the equation of the line passing through the point (1,2,-4) and perpendicualr to two lines (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y+29)/(8)=(z-5)/(-5) .

Find the angle between the lines (x-5)/(7)=(y+2)/(-5)=(z-9)/(1) and (x-5)/(2)=(y-10)/(2)=(z-9)/(-4) .

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/1=(z-6)/(-5) are at right angle, then find the value of k .

Show that the lines (x-5)/(4)=(y-7)/(4)= (z+3)/(-5) and (x-8)/(7)=(y-4)/(1) = (z-5)/(3) . are coplanar

The shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1)and(x+3)/(-3)=(y+7)/(2)=(z-6)/(4) is

The angle between the straight lines (x-4)/(2)=(y-5)/(0)=(z-6)/(0) and (3-x)/(3)=(y-7)/(0)=(z-3)/(0) is -

Find the vector equation of line passing through the point (1,2,-4) and perpendicular to the two lines: (x-8)/3=(y+19)/(-16)=(z-10)/7a n d(x-15)/3=(y-29)/8=(z-5)/(-5)

The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1 and (x+3)/(-36)=(y-3)/2=(z-6)/4 is (A) (21 ,5/3,(10)/3) (B) (2,10 ,4) (C) (-3,3,6) (D) (5,7,-2)

Find the angle between the lines (x-7)/(2)=(y-6)/(3)=(z+2)/(-4) and (2-x)/(-1)=(y-9)/(5)=(z-12)/(4) .

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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Sample Questions for Competitive Examination
  1. The symmetrical from of the lines x+y+z-1=0 and 4x+y-2z+2=0 are -

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  2. The equation of line passing through the point vec(a) parallel to the ...

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  3. The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)...

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  4. Consider the lines (x-5)/(3)=(y-7)/(-16)=(z-3)/(7) and (x-9)/(3)=(y-13...

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  5. The distance of the point A(veca) from the line vec(r)=vec(b)+tvec(c)...

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  6. If the length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  7. If the shortest distance between the lines (x-1)/(1)=(y-1)/(1)=(z-1)/(...

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  8. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy xy=c^(...

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  9. A line passing through the point (1,1,1) from a tiangle of area sqrt(6...

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  10. The direction cosines of two lines satisfy the relations lamda(l+m)=n ...

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  11. Each question in this section contains statements given in two columns...

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  12. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

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  13. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

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  14. vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)...

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  15. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  16. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  17. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  18. Statement - I: The point A (1,0,7) is the mirror image of the point B(...

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  19. Statement - I : The lines vec(r)=hat(i)+hat(j)-hat(k)+S(3hat(i)-hat(j)...

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