Home
Class 11
MATHS
Let vec(a)=vec(i)+vec(j)+vec(k) and vec(...

Let `vec(a)=vec(i)+vec(j)+vec(k) and vec(b)=2vec(i)+3vec(j)+vec(k)`. Find
(i) The projection vector of `vec(b)` on `vec(a)` and its magnitude.

Text Solution

Verified by Experts

The correct Answer is:
(i) `2sqrt(3)` units.
(ii) `vecj-veck`.
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE 5(a) II|5 Videos

  • PRODUCT OF VECTORS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE 5(a) III|4 Videos

  • PAIR OF STRAIGHT LINES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 4(c) III. |3 Videos

  • PROPERTIES OF TRIANGLES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES ( EXERCISE - 10(b) ) III.|11 Videos

Similar Questions

Explore conceptually related problems

If vec(a)= 2vec(i)-vec(j) +vec(k), vec(b)= 3vec(i) + 4vec(j) -vec(k) , then |vec(a) xx vec(b)|=

If vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k) , then find (vec(a) + vec(b)) xx (vec(a) - vec(b)) .

If vec(a)= 3 vec(i)- vec(j)-2vec(k), vec(b)= 2vec(i) + 3vec(j) + vec(k) , then (vec(a) + 2vec(b)) xx (2vec(a) - vec(b)) =

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0) , then

If vec(a)= 2vec(i) + 5vec(j) + vec(k) and vec(b)=4vec(i) + mvec(j) + n vec(k) are collinear vectors, then find the m and n

Given vec(a) = vec(i) + vec(j)-vec(k), vec(b)= - vec(i) + 2vec(j) + vec(k) and vec(c )= -vec(i) + 2vec(j) -vec(k) . A unit vector perpendicular to both vec(a) + vec(b) and vec(b) + vec(c ) is

If vec(a) = vec(i) + 2vec(j) - 3vec(k), vec(b)= 2vec(i) + vec(j) - vec(k) and vec(u) is a vector satisfying vec(a) xx vec(u) = vec(a) xx vec(b) and vec(a).vec(u)= 0 , then 2|vec(u)|^(2) =

If vec(c ) is a unit vector perpendicular to both vec(a) = vec(i) + 5vec(j) + vec(k) and vec(b)= 2vec(i) - vec(j) + vec(k) such that vec(a), vec(b), vec(c ) form right handed system then find vec(c ) .

If vec(a).vec(i)=4 , then (vec(a) . vec(j))xx (2vec(j)-3vec(k)) =

If vec(a)= 2vec(i) + 3vec(j)- 5vec(k), vec(b)= m vec(i) + n vec(j) + 12 vec(k) and vec(a) xx vec(b) = vec(0) then (m, n)=

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PRODUCT OF VECTORS-SOLVED PROBLEMS
  1. Let vec(a)=vec(i)+vec(j)+vec(k) and vec(b)=2vec(i)+3vec(j)+vec(k). Fin...

    Text Solution

    |

  2. If veca=6veci+2vecj+3veck and vecb=2veci-9vecj+6veck then find veca.ve...

    Text Solution

    |

  3. If bar(a)=bar(i)+2bar(j)-3bar(k)and bar(b)=3bar(i)-bar(j)+2bar(k) , th...

    Text Solution

    |

  4. IF | veca + vecb|=| veca - vecb| , then what is the angle betwe...

    Text Solution

    |

  5. If |veca|=11,|vecb|=23 and |veca-vecb|=30, then find the angle between...

    Text Solution

    |

  6. If veca=veci-vecj-veck and vecb=2veci-3vecj+veck, then find the projec...

    Text Solution

    |

  7. If P, Q, R and S are points whose position vectors are bari-bark, -bar...

    Text Solution

    |

  8. If vectors lambda bar(i) - 3bar(j)+5bar(k), 2lambda bar(i) - lambdabar...

    Text Solution

    |

  9. Let veca=2veci+3vecj+veck,vecb=4veci+vecj and vec(c)=veci-3vecj-7veck....

    Text Solution

    |

  10. Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk f...

    Text Solution

    |

  11. P.T the smaller angle theta between any two diagonals of a cube is giv...

    Text Solution

    |

  12. Let bara,barb,barc be non-zero mutually orthogonal vectors. If xbara+y...

    Text Solution

    |

  13. Let bara, barb and barc be mutually orthogonal vectors of equal magnit...

    Text Solution

    |

  14. The vectors bar(AB) = 3bari - 2barj + 2bark and bar(BC) = -bari - 2bar...

    Text Solution

    |

  15. Find the Cartesian equation of the plane passing through the point (-2...

    Text Solution

    |

  16. Find the cartesian equation of the plane through the point A (2,-1,-4)...

    Text Solution

    |

  17. Find the angle between the planes 2x-3y-6z=5 and 6x+2y-9z = 4.

    Text Solution

    |

  18. Find unit vector orthogonal to the vector 3bari + 2barj + 6bark and co...

    Text Solution

    |

  19. If veca=2veci-3vecj+5veck,vecb=-veci+4vecj+2veck, then find vecaxxvecb...

    Text Solution

    |

  20. If bar(a)=2bar(i)-3bar(j)+5bar(k),bar(b)=-bar(i)+4bar(j)+2bar(k), then...

    Text Solution

    |

  21. Find the area of the parallelogram for which the vectors veca=2veci-3v...

    Text Solution

    |