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Three vectors a=hati+hatj-hatk, b=-hati+...

Three vectors `a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-hatk`, then the unit vector perpendicular to both `a+b` and `b+c` is

A

`(hati)/(sqrt3)`

B

`6hatk`

C

`(hatk)/(sqrt3)`

D

`(hati+hatj+hatk)/(sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(a+b) xx (b+c)=3hatj xx (-2hati+4hatj)=6hatk`
So, required unit vector is `6hatk`.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-VECTORS -(VECTORS ) Exercise 2 ( Topical problems )
  1. If a,b,c ar enon-coplanar vectors and lamda is a real number, then the...

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  2. Vectors a and b are such that |a|=1,|b|=4 and a.b=2." If " c=2axxb-3b,...

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  3. Three vectors a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-h...

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  4. Given a parallelogram ABCD. If |vec(AB)|=a, |vec(AD)| = b & |vec(AC)| ...

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  5. Let a=a(1)hati+a(3)hatk, b=b(1)hati+b(3)hatk, c=c(1)hati+c(2)hatj+c(3)...

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  6. If vecu and vecv are unit vectors and theta is the acute angle bet...

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  7. If sum of two unit vectors is a unit vector; prove that the magnitude ...

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  8. The three vectors a, b and c with magnitude 3, 4 and 5 respectively an...

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  9. The vectors (a,a+1, a+2)(a+3, a+4, a+5)(a+6, a+7, a+8) are coplanar fo...

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  10. If a=hati+2hatk+3hatk, b=-hati+2hatj = hatk and c=3hati+hatj, then p s...

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  11. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

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  12. If a=lambdahati+2hatj-3hatk, b=2hati+lambdahatj-hatk, c=hati+2hatj+hat...

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  13. Three point A, B and C with position vectors a(1)=3hati-2hatj-hatk, a(...

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  14. If a and b are two vectos such that a.b lt 0 and |a.b|=|axxb|, then th...

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  15. If the position vectors off A,B,C and D are 2hati+hatj,hati-3hatj,3hat...

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  16. The vectors a=2hati+hatj-2hatk, b=hati+hatj. If c is a vector such tha...

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  17. If [[axxb,bxxc, c xxa]]=lambda[[a, b, c]]^(2), then lambda is equal t...

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  18. The vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the ...

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  19. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

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  20. If veca=1/(sqrt(10))(3hati+hatk),vecb=1/7(2hati+3hatj-6hatk), then the...

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