Home
Class 11
MATHS
P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2...

`P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1),` then find the projection length of ` vec P Qon vec R Sdot`

Text Solution

Verified by Experts

`vec( PQ)=vec(OQ)-vec(OP)=hati -2hatk`
`vec(RS)=vec(OS)-vec(OR)=4hati - 4hatj-hatk`
Projection of `vec(PQ) on vec(RS)= (vec(QP)vec(RS))/(|vec(RS)|) = 6/sqrt33`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.2|15 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.3|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Multiple Question)|11 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1255 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|288 Videos

Similar Questions

Explore conceptually related problems

A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0) . The angle beween the faces OPQ and PQR is :

Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find a vector having the same direction as that of vec A B and magnitude equal to | vec A C|dot

If [(0,p,3),(2,q^(2),-1),(r,1,0)] is skew- symmetric, find the values of p,q, and r.

If [{:(0,p,3),(2,q^2 , -1),(r, 1,0):}] is skew-symmetric , find the values of p , q and r

Consider the triangle ABC with vertices A(1,2,3) , B(-1, 0, 4) and C(0, 1, 2) (a) Find vec (AB) and vec (AC) Find angle A . (c) Find the area of triangle ABC.

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) Find the area of trianglePQR .

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) Find the coordinates of N, the mid-point of QR.

On the xy plane where O is the origin, given points, A(1,0), B(0,1) and C(1,1). Let P,Q, and R be moving points on the line OA, OB, OC respectively such that vec(OP)=45t(vec(OA)), vec(OQ)=60t(vec(OB)), vec(OR)=(1-t)(vec(OC)) with t gt 0 . If the three points P,Q and R are collinear then the value of t is equal to

CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.1
  1. Find |veca|and|vecb|, if (veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|.

    Text Solution

    |

  2. Show that |veca|vecb+|vecb|veca is perpendicular to |veca|vecb-|vecb|...

    Text Solution

    |

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

    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, suc...

    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 60^(@) . Then find ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If the vectors 3vecP+vecq, 5vecP - 3vecq and 2 vecp+ vecq, 4 vecp - 2v...

    Text Solution

    |

  13. Let vecA and vecB be two non-parallel unit vectors in a plane. If (alp...

    Text Solution

    |

  14. If veca,vecb,vecc are three vectors such that veca+2vecb+vecc=vec0 and...

    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 d...

    Text Solution

    |

  17. If |veca|=5 , |veca-vecb| = 8 and |veca +vecb|=10 then find |vecb|

    Text Solution

    |

  18. If A ,B ,C ,D are four distinct point in space such that A B is not...

    Text Solution

    |