Home
Class 12
MATHS
Find |veca|and |vecb|, if (veca+vecb).(v...

Find `|veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb|`

Text Solution

Verified by Experts

`(veca+vecb) .(veca-vecb) =8`
`or veca.veca-veca.vecb+vecb.veca-vecb.vecb=8`
`or |veca|^(2) -|vecb|^(2)=8`
`or (8|vecb|)^(2)-|vecb|^(2)=8 " " [|veca|=8|vecb|]`
`or |vecb|=sqrt(8/63)`
`or |veca|=8|vecb|=(8xx2sqrt2)/(3sqrt7)= (16sqrt2)/(3sqrt7)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.3|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

Find |veca|and|vecb| , if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb| .

if veca xx vecb = vecc ,vecb xx vecc = veca , " where " vecc ne vec0 then (a) |veca|= |vecc| (b) |veca|= |vecb| (c) |vecb|=1 (d) |veca|=|vecb|= |vecc|=1

Find |veca-vecb| , if two vectors vecaandvecb are such that |veca|=2,|vecb|=3andveca*vecb=4 .

If |vecb|=4 and (veca+vecb)*(veca-vecb)=9 , then the value |veca| is -

Prove that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) .

Find veca.vecb if |veca|=3, |vecb|=5,and |vecaxxvecb|=12

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |veca||vecb||vecc| holds if and only if

Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb)

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

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...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  8. If the angle between unit vectors veca and vecb is 120^(@) . Then find...

    Text Solution

    |

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

    Text Solution

    |

  10. A , B , C , D are any four points, prove that vec A Bdot vec C D+ v...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Find |veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb...

    Text Solution

    |

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

    Text Solution

    |