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If direction angles of a line are alpha,...

If direction angles of a line are `alpha, beta, gamma` such that `alpha+beta=90^(@)`, then `(cos alpha+cos beta+cos gamma)^(2)=`

A

`1-cos 2 alpha`

B

`1+cos 2 alpha`

C

`1-sin 2 alpha`

D

`1+sin2alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
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NIKITA PUBLICATION-THREE DIMENSIONAL GEOMETRY -MULTIPLE CHOICE QUESTIONS
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  2. A line makes angles alpha,betaa n dgamma with the coordinate axes. If ...

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  3. If direction angles of a line are alpha, beta, gamma such that alpha+b...

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  4. A line lies in XZ-plane and makes an angle 60^(@) with Z-axis, find i...

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  7. Which of the following is false ?

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  8. Which of the following is true ?

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  9. If a line makes angles 90^@, 135^@, 45^@ with X,Y and Z axes respectiv...

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  10. The direction cosines of the line which bisects the angle between posi...

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  11. The direction consines of a line equally inclined with the co-ordinate...

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  12. Of line makes angle 60^(@), 120^(@), 45^(@) with X, Y, Z axes respecti...

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  13. If the line makes angles 45^(@), 60^(@), 120^(@) with X, Y, Z axes res...

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  14. The direction cosines of a line which makes an angle of 45^(@) with Z-...

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  15. The direction consines of a line which lies in XZ-plane and making an ...

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  16. If alpha,beta, gamma are the direction angles of a vector and cos alph...

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  17. A line makes the some angle theta with each of the x and z-axes. If t...

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  18. If the direction cosines of a line are p,-p, (-p)/(2), then p =

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  19. If 1/2,1/3,n are direction cosines of a line, then the value of n is

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  20. If (1)/(sqrt(2)),(1)/(2), n are the direction consines of a line, then...

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