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A line line makes the same angle theta w...

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

A

`(2)/(3)`

B

`(1)/(5)`

C

`(3)/(5)`

D

`(2)/(5)`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-THREE DIMENSIONAL GEOMETRY -Critical Thinking
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  2. Show that no line in space can make angles (pi)/(6) and (pi)/(4) with ...

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  3. A line line makes the same angle theta with each of the x and z-axes....

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  4. The projections of a line on the co-ordinate axes are 4,6,12. The dire...

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  5. If P(x,y,z) is a point in space at a distance r from the origin O, the...

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  6. A line AB is inclined to OX at 45^(@) and to OY at 60^(@) and let P be...

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  7. The vector of magnitude 6 which is equally inclined to the co-ordinate...

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  8. If O is the origin, O P=3 with direction ratios -1,2,a n d-2, then fin...

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  9. Line with direction ratios 1, 1, 1 is

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  10. The angle made by the vector 3hati-4hatj+5hatk with the Z-axis is

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  11. A line passes through the point (6, -7, -1) and (2, -3, 1). The direct...

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  12. If first two numbers of the direction cosines of a line joining points...

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  13. If the points (2,a,-1),(3,4,b)and(1,-2,3) are collinear, the values of...

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  14. If (1,a,1),(3,-1,2)and(1,a^(2),1) are collinear, then the values of a ...

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  15. Points (-2, 4, 7), (3, -6 -8) and (1, -2, -2) are

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  16. If the angle between the lines whose direction cosines are a,(-2)/(3),...

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  17. The acute angle between the lines having direction ratios 5,4,1 and -3...

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  18. Find the angle between the lines whose direction ratios are: 2,-3,4 ...

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  19. Let theta be the angle between the lines AB and AC, where A, B and C a...

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  20. The direction cosines l, m and n of two lines are connected by the rel...

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