Home
Class 12
MATHS
If in triangle A B C , vec A B= vec u/(|...

If in triangle `A B C , vec A B= vec u/(| vec u|)-- vec v/(| vec v|)a n d vec A C=(2 vec u)/(| vec u|),w h e r e| vec u|!=| vec v|,` then `1+cos2A+cos2B+cos2C=0` b.`sinA=cos C` c. projection of `A C` on `B C` is equal to `B C` d. projection of `A B` on `B C` is equal to `A B`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If in triangle ABC,vec AB=(vec u)/(|vec u|)-(vec v)/(|vec v|) and vec AC=(2vec u)/(|vec u|), where |vec u|!=|vec v| then 1+cos2A+cos2B+cos2C=0 b.sin A=cos C c. projection of AC on BC is equal to BC d.projection of AB on BC is equal to AB

vec u = vec a-vec b, vec v = vec a + vec b and | vec a | = | vec b | = 2 then | vec u xxvec v | is equal to

vec a * {(vec b + vec c) xx (vec a + 2vec b + 3vec c)} = [vec with bvec c]

If vec a xxvec b = vec b xxvec c = vec c xxvec a, then vec a + vec b + vec c is equal to

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If vec( A) + vec(B) =vec( C ) , and | vec(A)| =2 | vec( B) | and vec( B). vec( C ) = 0 , then

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

RESONANCE DPP-JEE MAINS-All Questions
  1. Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...

    Text Solution

    |

  2. ((dy)/(dx))^(2) + 2y cot x (dy)/(dx) = y^(2) has the solution

    Text Solution

    |

  3. If in triangle A B C , vec A B= vec u/(| vec u|)-- vec v/(| vec v|)a n...

    Text Solution

    |

  4. A,B,C are three events for which P(A)=0. 4 ,P(B)=0. 6 ,P(C)=0. 5 ,P(Au...

    Text Solution

    |

  5. If z is complex number such that |(6z-i)/(2+3i z)|lt=1 , then which of...

    Text Solution

    |

  6. If vec a= hat i+ hat j+ hat k , vec adot vec b=2 and vec ax vec b=2 ...

    Text Solution

    |

  7. Let P and Q be two statements, then ~(~P^^Q)^^(PvvQ) is logically equi...

    Text Solution

    |

  8. If the circle x^2+y^2 -2x-2y+1=0 is inscribed in a triangle whose two...

    Text Solution

    |

  9. Let P M be the perpendicular from the point P(1,2,3) to the x-y pla...

    Text Solution

    |

  10. Tangents PA and PB are drawn to the circle x^2+y^2=4,then locus of the...

    Text Solution

    |

  11. If LdotCdotM of two positive numbers aa n db is p^3q^2r where p ...

    Text Solution

    |

  12. Find the equation of the circle which is touched by y=x , has its cent...

    Text Solution

    |

  13. If g(x)=(4cos^4x-2cos2x-1/2cos4x-x^7)^(1/7) then the value of g(g(100)...

    Text Solution

    |

  14. A(1, 2) and B(7, 10) are two points. If P(x) is a point such that the ...

    Text Solution

    |

  15. The line y=x is tangent at (0, 0) to a circle of radius 1. The centre ...

    Text Solution

    |

  16. If H is the orthocenter of DeltaABC and if AH = x, BH = y, CH = z, t...

    Text Solution

    |

  17. C1 and C2 are fixed circles of radii r1 and r2 touches each other ext...

    Text Solution

    |

  18. Let zk be the roots of the equation (z+1)^7+z^7=0, then sum (k=0)^6 Re...

    Text Solution

    |

  19. Find the equations of the sides of the triangle having (3, - 1) as a v...

    Text Solution

    |

  20. The equation of the circle which passes through the point A(0, 5) and ...

    Text Solution

    |