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If P(x,y,z) is a point in space at a dis...

If `P(x,y,z)` is a point in space at a distance r from the origin O, then the direction cosines of the line OP are

A

`(r)/(x),(r)/(y),(r)/(z)`

B

`rx,ry,rz`

C

`(x)/(r),(y)/(r),(z)/(r)`

D

`r^(2)x,r^(2)y,r^(2)z`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-THREE DIMENSIONAL GEOMETRY -Critical Thinking
  1. A line line makes the same angle theta with each of the x and z-axes....

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the angle between the line whose direction cosines are given ...

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  20. The direction cosines of a line equally inclined to three mutually per...

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