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The vector veca=alpha hati+2hatj+betahat...

The vector `veca=alpha hati+2hatj+betahatk` lies in the plane of vectors `vecb=hati+hatj and vecc=hatj+hatk` and bisects the angle between `vecb and vecc`. Then which one of the following gives possible values o `alpha and beta? (A) `alpha=2, beta=1` (B) `alpha=1, beta=1` (C) `alpha=2, beta=1` (D) `alpha=1, beta=2`

A

`alpha = 2, beta = 2`

B

`alpha = 1, beta = 2`

C

`alpha = 2, beta = 1`

D

`alpha = 1, beta = 1`

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The correct Answer is:
D
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DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -1 : CONCEPT BUILDER
  1. Let vec a, vec b and vec c are vectors of magnitude 3,4,5 respectively...

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  2. If veca , vecb , vec c are any three coplanar unit vectors , then :

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  3. The vector veca=alpha hati+2hatj+betahatk lies in the plane of vectors...

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  4. Let vecu= hati+hatj, vecv = hati -hatj and vecw = hati+2hatj+3hatk. I...

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  5. If vectors a=4hat(i)-3hat(j)+6hat(k) and vector b=-2hat(i)+2hat(j)-hat...

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  6. A vector of magnitude 14 lies in the xy-plane and makes an angle of 60...

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  7. If veca,vecb,vec c are unit vectors such that veca+vecb+vec c= vec0 fi...

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  8. The two variable vectors 3xhati+yhatj-3hatk and xhati-4yhatj+4hatk are...

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  9. Angle between the vectors sqrt3(veca xx vec b) " and " vec b - (veca ....

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  10. If the vector veca = (2 ,log3 x ,a ) and vecb = (-3,a log3x,log3x) are...

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  11. If veca , vecb ,vec c are the 3 vectors such that |veca| = 3, |vecb| ...

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  12. The vectors (2hati - mhatj+ 3mk) and {(1 + m) hati -2m hatj + hatk} i...

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  13. Let veca , vecb , vecc be three unit vectors such that |veca + vecb +...

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  14. If veca,vecb and vecc are three vectors of which every pair is non col...

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  15. The two vectors (x^2 - 1)hati +(x+2)hatj + x^2 hatk and 2hati -xhatj +...

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  16. The value of 'a' for which the points A, B,C with position vectors ...

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  17. For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxx...

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  18. If (veca xx vecb) xx vecc = vec a xx (vecb xx vecc), where veca, vecb ...

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  19. veca=3hati-5hatj and vecb=6hati+3hatj are two vectors and vec c is a v...

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  20. Vectors veca and vec b are inclined at an angle theta = 120^@ . If |ve...

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