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The angle between the lines barr = (4, -...

The angle between the lines `barr = (4, -3, 2) + k(2, 1, 2), k epsilon R` and `barr= (2, 0, 5) + k(6, 3, 2), k epsilon R` is .......

A

`sin^(-1)""(4sqrt5)/(21)`

B

`cos^(-1)""(4sqrt5)/(21)`

C

`cos^(-1)""(4sqrt5)/(19)`

D

`sin^(-1)""(19)/(21)`

Text Solution

Verified by Experts

The correct Answer is:
A
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The angle between the lines bar = (-3,5,-1) + k(1,2,1), k in R and bar r = (1,3,-2) + k (6,-3,0), k in R is ....

If the lines barr = (2, -3, 7) + k(2, a, 5), k epsilon R and barr = (1, 2, 3) + k(3, -a, a), k epsilon R are perpendicular to each other then a = ......

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If the line bar r = (5,5,2) + k (3,6,9) k in R and bar = (0,3,-1) + k (1,2,b), k in R are parallel then b = ...... .

Find the distance between the points (k, k+1, k+2) and (0, 1, 2).

The angle between the planes bar.r (1,2,-1) = 3 and 2x -y + 2z = 2 is .......... .

If the vector equation of the line is barr = (1, -5,9) + k(2, 2, -1), k epsilon R then its cartesian equation is .........

The image of the point (1, 2, 3) in the line barr = (6, 7, 7) + k (3, 2,-2), k epsilon R is (5, 8, a) then a = ….............

The equation of the line passing through hat i + 3 hat j + 2 hat k and prependiccular to the lines bar (r) = (1,2,-1) +lambda (2,1,1) and bar r = (2,6,1) + mu (1,2,3) is .........

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MULTIPLE CHOICE QUESTIONS (MCQs)
  1. If the vector equation of the line is barr= (1, -5,9) + k(2, 2, -1), k...

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  2. If the cartesian equation of the line (2-x)/(4)=(y-3)/(-2),z+4=0 then ...

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  3. The angle between the lines barr = (4, -3, 2) + k(2, 1, 2), k epsilon ...

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  4. The equation of line perpendicular to barr. (1, 2, 1) = 4 and passing ...

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  5. The symmetric equation of the line passing through (3, 1, - 1) and (3,...

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  6. The equation of the line passes through (2,-3,5) and makes equal with ...

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  7. If the lines (x-2)/(k)=(y-8)/(-3)=(z+5)/(9) and (x-5)/(1)=(y+2)/(1)=(z...

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  8. If the lines (x-1)/(1)=(y-4)/(c)=(z+3)/(-3) and (x+1)/(-c)=(y-3)/(2)=(...

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  9. The vector form of the line 3x + 1 = 62 – 2, y - 1 = 0 is .........

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  10. The lines x=(y-1)/(1)=(z+1)/(3) and {(2,1+3k,2+k)//k epsilon R} are …....

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  11. The perpendicular distance of the point (3, -4, -5) from the line (x-2...

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  12. The image of the point (1, 2, 3) in the line barr = (6, 7, 7) + k (3, ...

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  13. If the line bar r = (5,5,2) + k (3,6,9) k in R and bar = (0,3,-1) + ...

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  14. The angle between the lines bar = (-3,5,-1) + k(1,2,1), k in R and bar...

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  15. The angle between the lines whose direction cosines are given by l + ...

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  16. The cartesian equation of the line passing through (2,2,-3) and (1,3,5...

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  17. The equation of the line passes through (2,-3,5) and makes equal with ...

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  18. The angle between the lines whose direction cosines are l, m, n and m-...

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  19. The vector equation of the line (3-x)/(3) = (2y - 3)/(5) = z/2 is .......

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  20. The lines bar r = (-1,2,5) + k (-1,2,5), k in R and bar r = (-3,1,5) ...

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