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A line makes the same angle theta, with ...

A line makes the same angle `theta`, with each of the x and z axis. If the angle `beta`, which it makes with y-axis, is such that `sin^(2)beta=3sin^(2)theta, " then " cos^(2)theta=`

A

`2//3`

B

`2//5`

C

`3//5`

D

`1//5`

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DIPTI PUBLICATION ( AP EAMET)-DIRECTION COSINES AND DIRECTION RATIOS-EXERCISE 1
  1. If alpha, beta, gamma are the angles made by a line with the positive ...

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  2. If a line in the space makes angles alpha, beta, " and " gamma with th...

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  3. A line makes the same angle theta, with each of the x and z axis. If t...

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  4. A line AB in three-dimensional space makes angles 45^(@) " and " 120^(...

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  5. A straight line is equally inclined to all the three coorinate axes. T...

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  6. The number of lines which are equally inclined to the coordinate axes ...

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  7. The d.c.'s of a line which is equally inclined to the coordinate axes ...

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  8. If the d.r.'s of a line are (3, -4, 12) then d.c.'s of the line are

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  9. The d.c.'s of the line joining the points A(4, 3, 1), B(-2, 1, -2) are

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  10. If (l(1),m(1),n(1)),(l(2),m(2),n(2)) are d.c's of two lines then find ...

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  11. If (2, 1, -1) and (1, -1, -1) are direction ratios of two lines, then ...

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  12. IF the d.r.'s of oversetharr(OA),oversetharr(OB) are (1, -2, -1), (3, ...

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  13. The direction ratios of two lines AB, AC are 1, -1, -1 and 2, -1, 1. T...

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  14. If (a(1), b(1), c(1)), (a(2), b(2), c(2)) are d.r.'s of two perpendicu...

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  15. If (a(1), b(1), c(1)), (a(2), b(2), c(2)) are d.r.'s of two perpendicu...

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  16. If the direction cosines of any two lines are (-2/3, 1/3, 2/3), (3/5, ...

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  17. The angle between the lines whose direction cosines are (sqrt(3)//4, 1...

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  18. If P(2, 3, -6), Q(3, -4, 5) are two points, then anglePOQ is

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  19. If P = (0, 1, 2), Q = (4, -2, 1), O = (0, 0, 0) then anglePOQ=

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  20. The cosine of the angle A of the triangle with vertices A(1, -1, 2), B...

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