Home
Class 12
MATHS
Express bar(p) as a linear combination o...

Express `bar(p)` as a linear combination of `bar(a),bar(b)andbar(c)`, where `bar(p)=hat(i)+4hat(j)-4hat(k),bar(a)=2hat(i)-hat(j)+3hat(k),bar(b)=hat(i)-2hat(j)+4hat(k),bar(c)=-hat(i)+3hat(j)-5hat(k)`.

Text Solution

Verified by Experts

The correct Answer is:
`bar(p)=bar(a)+2bar(b)+3bar(c)`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple choice question|10 Videos

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple Choice Questions|12 Videos

Similar Questions

Explore conceptually related problems

Find bar(a). bar(b) xx bar(c) , if bar(a) = 3 hat(i) - hat(j) + 4 hat(k), bar(b) = 2hat(i) + 3 hat(j) - hat(k), bar(c) = - 5 hat(i) + 2 hat(j) + 3 hat(k)

If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

If bar(a)=3hat(i)-2hat(j)+7hat(k),bar(b)=5hat(i)+hat(j)-2hat(k)andbar(c)=hat(i)+hat(j)-hat(k) , then find bar(a)*(bar(b)xxbar(c)) .

Find [bar(a)bar(b)bar(c)] where : (1) bar(a)=2hat(i)+hat(j)-hat(k),bar(b)=3hat(i)-hat(j)-hat(k),hat(c)=hat(j)+3hat(k) (2) bar(a)=7hat(i)-hat(j)+2hat(k),bar(b)=hat(i)+3hat(j)-hat(k),bar(c)=4hat(i)+5hat(k) .

Find lamda , if the vectors bar(a)=hat(i)+hat(j)+hat(k),bar(b)=hat(i)-hat(j)+hat(k)andbar(c)=2hat(i)+3hat(j)+lamdahat(k) are coplanar.

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

If bar(P)=hat i+hat j+hat k,bar(Q)=2hat i-hat j-hat k , then bar(P)-bar(Q) is

If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=hat(i)-hat(j)+4hat(k)andbar(a)*(bar(b)xxbar(c))=1 , then find the value of q.

If bar(a)=hat(i)+2hat(j),b=-2hat(i)+hat(j),bar(c)=4hat(i)+3hat(j) find x and y such bar(c)=xbar(a)+ybar(b) .

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

NAVNEET PUBLICATION - MAHARASHTRA BOARD-VECTORS-Examples for Practics
  1. If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(...

    Text Solution

    |

  2. If the points A(2,p,1),B(1,2,q) and C(3,2,1) are collinear, then find ...

    Text Solution

    |

  3. Express bar(p) as a linear combination of bar(a),bar(b)andbar(c), wher...

    Text Solution

    |

  4. Express the vector bar(a)=9hat(i)+hat(j)+2hat(k) as a linear combinati...

    Text Solution

    |

  5. If bar(a),bar(b),bar(c) are non-zero, non -coplanar vectors, then show...

    Text Solution

    |

  6. If bar(a)+lamdabar(b)+3bar(c),-2bar(a)+3bar(b)-4bar(c),bar(a)-3bar(b)+...

    Text Solution

    |

  7. D, E, F are the midpoints of the sides BC, CA and AB respectively of t...

    Text Solution

    |

  8. Show that if bar(AB)=bar(DC), then the figure ABCD is a parallelogram.

    Text Solution

    |

  9. If G is the centroid of triangleABC and O is any point in the plane of...

    Text Solution

    |

  10. Find [bar(a)bar(b)bar(c)] where : (1) bar(a)=2hat(i)+hat(j)-hat(k),b...

    Text Solution

    |

  11. If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=ha...

    Text Solution

    |

  12. Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2...

    Text Solution

    |

  13. Find the volume of the parallelopiped whose coterminus edges are : (...

    Text Solution

    |

  14. Find lamda, if the vectors bar(a)=hat(i)+hat(j)+hat(k),bar(b)=hat(i)-h...

    Text Solution

    |

  15. If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)...

    Text Solution

    |

  16. Find the volume of the parallelopiped with segments AB, AC and AD as c...

    Text Solution

    |

  17. Find the volume of the tetrahedron whose vertices are A(3,7,4),B(5,-2,...

    Text Solution

    |

  18. Find the volume tetrahedron whose coterminus edges are 7hat(i)+hat(k),...

    Text Solution

    |

  19. Show that the following sets of points are coplanar : (1) (3,9,4),(0...

    Text Solution

    |

  20. Find the value of x, if the points A(3,2,1),B(4,x,5),C(4,2,2)andD(6,5,...

    Text Solution

    |