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If a vector vec(A) make angles alpha , b...

If a vector `vec(A)` make angles `alpha , beta ` and `gamma`, respectively , with the `X , Y` and `Z` axes , then `sin^(2) alpha + sin^(2) beta + sin^(2) gamma =`

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 1`
`1 - sin^(2) alpha + 1 - sin^(2) beta + 1 - sin^(2) gamma = 1`
`sin^(2) alpha + sin^(2) beta + sin^(2) gamma = 2`
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CP SINGH-VECTORS-Excercises
  1. The unit vector parallel to the resultant of the vectors vec(A) = hat(...

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  2. If vec(A) = 3 hat(i) + 6 hat(j) - 2hat(k) , the directions of cosines ...

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  3. If a vector vec(A) make angles alpha , beta and gamma, respectively ,...

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  4. If the sum of two unit vectors is a unit vector,then find the magnitud...

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  5. What is the angle between vec(A) and the esultant of (vec(A) + vec(B))...

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  6. A paricle starting from the origin (0,0) moves in a straight line in (...

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  7. If for two vectors vec(A) and vec(B), sum (vec(A)+vec(B)) is perpendic...

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  8. If a vector 2 hat (i) + 3 hat(j) + 8 hat(k) is perpendicular to the ve...

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  9. Which of the following vectors is//are perpendicular to the vector 4 I...

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  10. If vec(A) = 2 I + j - k , vec(B) = I + 2 j + 3 k , and vec(C ) = 6 i -...

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  11. Vectors which is perpendicular to ( a cos theta hat (i) + b sin theta ...

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  12. Two vectors vec A and vecB have equal magnitudes.If magnitude of (vecA...

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  13. The position vector of a particle is vec( r) = a cos omega t i + a sin...

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  14. The component of vector A= 2hat(i)+3hat(j) along the vector hat(i)+hat...

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  15. The vector component of vector vec(A) = 3 hat(i) + 4 hat(j) + 5 hat(k)...

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  16. If vec(A)xxvec(B)=vec(C ), then which of the following statements is w...

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  17. The magnitude of the vectors product of two vectors |vecA| and |vecB| ...

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  18. Three vector vec(A),vec(B), vec(C ) satisfy the relation vec(A)*vec(B)...

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  19. A vector vec(A) is along the positive x- axis . If B is another vector...

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  20. A vector vec(A) points verically upward and vec(B) points towards nort...

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