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If a line makes angles `alpha,beta,gamma` with the axes respectively tehn `cos2alpha+cos2beta+cos2gamma=` `-2` b. `-1` c. `1` d. 2

A

2

B

-1

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`l=cos alpha, cosb` and `n=cos gamma`
`:.l^(2)+m^(2)+n^(2)=1`
`impliescos^(2) alpha+cos^(2)beta+cos^(2)gamma=1`
`implies(1+cos 2alpha)/2+(1+cos 2 beta)/2+(1+cos 2gamma)/2=1`
`impliescos 2 alpha+cos 2 beta+cos 2gamma=-1`
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OBJECTIVE RD SHARMA ENGLISH-THREE DIMENSIONAL COORDINATE SYSTEM -Exercise
  1. If a line makes angles alpha,beta,gamma with the axes respectively teh...

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  2. If the x-coordinate of a point P on the join of Q(2,2,1)a n dR(5,1,-...

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  3. The distance of the point P(a,b,c) from the x-axis is

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  4. Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2...

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  5. If P (3,2,−4) , Q (5,4,−6) and R (9,8,−10)  are collinear, then  ...

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  6. A (3,2,0) , B (5,3,2)C (-9,6,-3) are three points forming a triangle. ...

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  7. A line passes through the points (6,-7,-1)a n d(2,-3,1)dot Find te ...

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  8. If a line makes angles alpha,beta,gamma with the positive direction of...

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  9. If P is a point in space such that OP=12 and vec(OP) is inclied at ang...

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  10. A vector vec O P is inclined to O X at 45^0 and O Y at 60^0 . Find th...

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  11. vector is equal inclined with the coordinate axes. If the tip ofvecr ...

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  12. If vecr is a vector of magnitude 21 and has direction ratios 2, -3 an...

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  13. The direction cosines of the lines bisecting the angle between the lin...

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  14. Find the coordinates of the foot of the perpendicular drawn from po...

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  15. The projections of a line segment on the coordinate axes are 12,4,3 re...

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  16. If P(x,y,z) is a point on the line segment joining Q(2,2,4) and R(3,5,...

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  17. If O is the origin, OP = 3, with direction ratios -1, 2 and -2, then f...

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  18. A mirror and a source of light are situated at the origin O and at a p...

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  19. Find the angle between any two diagonals of a cube.

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  20. A line makes angles angle, beta, gamma and delta with the diagonals of...

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  21. If P(0,1,2),\ Q(4,-2,1)a n d\ O(0,0,0) are three points then P O Q= ...

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