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The vector equations of two lines L1 and...

The vector equations of two lines `L_1 and L_2` are respectively, `L_1:r=2i+9j+13k+lambda(i+2j+3k) and L_2: r=-3i+7j+pk +mu(-i+2j-3k)` Then, the lines `L_1 and L_2` are

A

skew lines all `p in R`

B

intersecting for all `p in R` and the point of intersection is `(-1, 3, 4)`

C

intersecting lines for `p=-2`

D

intersecting for all real `p in R`

Text Solution

Verified by Experts

The correct Answer is:
(c)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. A parallelopied is formed by planes drawn through the points (1, 2, 3)...

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  2. Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(...

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  3. The vector equations of two lines L1 and L2 are respectively, L1:r=2i+...

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  4. Consider the plane (x,y,z)= (0,1,1) + lamda(1,-1,1)+mu(2,-1,0) The dis...

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  5. The value of a for which the lines (x-2)/(1)=(y-9)/(2)=(z-13)/(3) and ...

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  6. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

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  7. Given planes P1:cy+bz=x P2:az+cx=y P3:bx+ay=z P1, P2 and P3 pass...

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  8. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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

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  10. The line which contains all points (x, y, z) which are of the form (x,...

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  11. If the three planes rcdotn1=p1, rcdotn2=p2 and rcdotn3=p3 have a commo...

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  12. The equation of the plane which passes through the line of intersectio...

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  13. A straight line is given by r=(1+t)i+3tj+(1-t)k, where tinR. If this l...

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  14. The distance of the point (-1, -5, -10) from the point of intersection...

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  15. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

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  16. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  17. The orthogonal projection A' of the point A with position vector (1, 2...

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  18. The equation of the line passing through (1, 1, 1) and perpendicular t...

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  19. A variable plane at a distance of 1 unit from the origin cuts the axes...

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  20. The angle between the lines AB and CD, where A(0, 0, 0), B(1, 1, 1), C...

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