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If |veca|=4 , |veca-vecb| = 6 and |veca ...

If `|veca|=4 , |veca-vecb| = 6 and |veca +vecb|=8` then find `|vecb|`

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`|veca+vecb|^(2)+|veca-vecb|^(2)= 2(|veca|^(2)+|vecb|^(2))`
`Rightarrow 100 + 64 = 2(25+|vecb|^(2))`
`or 82 = 25 + |vecb|^(2)`
`or |vecb|^(2) = 57`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.1
  1. Find |veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb...

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  2. Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a|...

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  3. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

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  4. If |a|=3,|b|=4a n d the angle between aa n db is 120^0 , then find the...

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  5. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

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  6. Let veca , vecb and vecc be pairwise mutually perpendicular vectors, s...

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  7. If vec a,vec b, vec c be three vectors such that vec a+vec b+vec c=0 ,...

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  8. If the angel between unit vectors vec aa n d vec b60^0 , then find...

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  9. Let vecu=hati+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn i...

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  10. A,B,C and d are any four points prove that vec(AB).vec(CD)+vec(BC).vec...

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  11. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projectio...

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  12. If the vectors 3 vec p+ vec q ;5p-3 vec qa n d2 vec p+ vec q ;3 vec p-...

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  13. Let vec A and vec B be two non-parallel unit vectors in a plane. If...

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  14. Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b...

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  15. If veca and vecb are unit vectors, then find the greatest value of |ve...

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  16. Constant forces P1= hat i+ hat j+ hat k ,P2= - hat i+2 hat j- hat ka n...

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  17. If |veca|=4 , |veca-vecb| = 6 and |veca +vecb|=8 then find |vecb|

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  18. If A ,B ,C ,D are four distinct point in space such that vec(A B) is...

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