Home
Class 12
MATHS
The vectors vec(a) " and " vec(b) are no...

The vectors `vec(a) " and " vec(b)` are non-collinear. If `vec(p)=(x+4y)vec(a)+(2x+y+1)vec(b)` and `vec(q)=(-2x+y+2)vec(a)+(2x-3y-1)vec(b)` satisfy the relation `3vec(p)=2vec(q)`, find the values of x and y.

Text Solution

Verified by Experts

The correct Answer is:
x=2, y=-1
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION|18 Videos

  • VECTOR

    CHHAYA PUBLICATION|Exercise EXERCISE - SHORT ANSWER TYPE QUESTIONS|17 Videos

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type )|2 Videos

Similar Questions

Explore conceptually related problems

The vectors vec a and vec b are non collinear. If vec p = (x+4y)veca+ (2x+y+1)vec b and vec q= (-2x+y+2)vec a+ (2x-3y-1)vec b satisfy the relation 3vec p= 2vec q find the values of x and y.

The vectors vec(a) " and " vec(b) are non-collinear. Find for what value of x, the vectors vec(c)=(x-7)vec(a)+2vec(b) "and " vec(d)=(2x+1)vec(a)-vec(b) are collinear.

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

Two vectors vec(a) and vec (b) are such that |vec(a).vec(b)| = |vec(a) xx vec(b)| , then find the angle between the vectors vec(a) and vec(b) .

If |vec(a)| = 2, |vec(b)| = 3 and vec (a) . vec(b) = 3 , then find the projection of vec(b)" on " vec(a)

If vec(a) and vec(b) are two vector such that |vec(a)| = 2, |vec(b)| =3 and vec(a).vec(b) =4 , then find the value of |vec(a)- vec(b)|

Let vec(a), vec(b) and vec(c) be three non-zero vectors such that no two of them are collinear and (vec(a) xx vec(b)) xx vec(c) = (1)/(3) |vec(b)||vec(c)| vec(a) . If theta is the angle between vector vec(b) and vec(c) , then a value of sin theta is

CHHAYA PUBLICATION-VECTOR-EXERCISE - LONG ANSWER TYPE QUESTIONS
  1. If vec(a)=hat(i)+hat(j)+hat(k), vec(b)=2hat(i)-hat(j)+3hat(k) " and " ...

    Text Solution

    |

  2. By vector method, show that the four points (7, 2, -3), (6, 1, 4), (-3...

    Text Solution

    |

  3. Find a unit vector in direction parallel to the sum of the vectors vec...

    Text Solution

    |

  4. If vec(a)=2hat(i)-2hat(j)+hat(k), vec(b)=2hat(i)+3hat(j)+6hat(k) " and...

    Text Solution

    |

  5. The vectors vec(a) " and " vec(b) are non-collinear. Find for what val...

    Text Solution

    |

  6. Given that the points with position vectors 12hat(i)-5hat(j), 10hat(i)...

    Text Solution

    |

  7. The vectors vec(a) " and " vec(b) are non-collinear. If vec(p)=(x+4y)v...

    Text Solution

    |

  8. If the sum of two unit vectors is a unit vector, prove that the magnit...

    Text Solution

    |

  9. ABCDEF is a regular hexagon. If vec(CD)=vec(a), vec(DE)=vec(b), " find...

    Text Solution

    |

  10. bar(AC) " and " bar(BD) are the diagonals of the parallelogram ABCD. P...

    Text Solution

    |

  11. By vector method show that the figure formed by joining the mid-points...

    Text Solution

    |

  12. Defination : Unit vector

    Text Solution

    |

  13. ABCD is a parallelogram and P is the midpoint of the side bar(BC). Pro...

    Text Solution

    |

  14. ABCD is a parallelogram, P and Q are the mid-points of the sides bar(A...

    Text Solution

    |

  15. ABCD is a parallelogram and P is the mid-point of bar(DC). If Q is a p...

    Text Solution

    |

  16. D, E, F are the midpoints of the sides bar(BC), bar(CA) " and " bar(AB...

    Text Solution

    |

  17. C is the midpoint of the line segment bar(AB) and O is any point outsi...

    Text Solution

    |

  18. G is a point inside the plane of the triangle ABC, if vec(GA)+vec(GB)+...

    Text Solution

    |

  19. The diagonals of the parallelogram ABCD intersect at E. If vec(a), vec...

    Text Solution

    |

  20. By vector method prove that the straight line joining the midpoints of...

    Text Solution

    |