Home
Class 12
MATHS
Prove that (vec a × vec b)^(2) = a^(2)b^...

Prove that `(vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2)`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

If vec a and vec b be perpendicular vectors, then prove that (vec a + vec b)^(2) = (vec a - vec b)^(2) .

Prove that (vec a × vec b).(vec c × vec d) = [[vec a.vec c,vec a.vec d],[vec b.vec c,vec b.vec d]] .

Prove that : [(vec a × vec b) (vec b × vec c) (vec c × vec a)] = [vec a vec b vec c]^(2) .

Show that (vec(a) xx vec(b))^(2) = |(vec(a).vec(a), vec(a).vec(b)),(vec(a).vec(b), vec(b).vec(b))| .

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .

Prove that vec(a) xx (vec(b) + vec(c)) + vec(b) xx (vec(c) + vec(a)) + vec(c) xx (vec(a) + vec(b)) = vec(0)

For any three vectors vec(a), vec(b) and vec(c) , prove that vec(a) xx (vec(b) - vec(c)) = (vec(a) xx vec(b)) - (vec(a) xx vec(c)) .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If f is periodic with period 3 and f(1) = 1 then what is the value of ...

    Text Solution

    |

  2. Evaluate int(-2)^2abs([x])dx .

    Text Solution

    |

  3. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

    Text Solution

    |

  4. Find the perpendicular distance of the point (-1,3,9) from the line (x...

    Text Solution

    |

  5. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .

    Text Solution

    |

  6. Find the equation of planes passing throught the points (6,-1,1), (5,1...

    Text Solution

    |

  7. Find the co-ordinates of the foot of the perpendicular drawn from the ...

    Text Solution

    |

  8. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

    Text Solution

    |

  9. If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y(n+2)+(2n+1)xy(n+1)+(...

    Text Solution

    |

  10. Show that the rectangle of maximum area that can be inscribed in a giv...

    Text Solution

    |

  11. Prove the following by vector method. Altitudes of a triangle are conc...

    Text Solution

    |

  12. Find the magnitude and equation of the line of shotest distance betwee...

    Text Solution

    |

  13. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

    Text Solution

    |

  14. Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(...

    Text Solution

    |

  15. Show that the function f : R^+toR^+ defined by f (x) =x+1/x is injecti...

    Text Solution

    |

  16. Solve "sin"^(-1)x-"cos"^(-1)x="cos"^(-1)sqrt(3)/(2)

    Text Solution

    |

  17. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

    Text Solution

    |

  18. Evaluate intln(x^2+x+2)dx

    Text Solution

    |

  19. int0^pi((xtanx)/(secx+tanx))dx

    Text Solution

    |

  20. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

    Text Solution

    |