Home
Class 12
MATHS
Show that (vecaxxvecb)^2 = a^2b^2 - (vec...

Show that `(vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2`.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2018

    SHARAM PUBLICATION|Exercise EXERCISE|46 Videos

  • QUESTION PAPER 2020

    SHARAM PUBLICATION|Exercise EXERCISE|47 Videos

Similar Questions

Explore conceptually related problems

Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbxxvecc)]^2 = a^2b^2c^2

Find veca*(vecaxxvecb).

If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and veca.vecb = 6, find |veca+vecb| and |veca-vecb| .

Find a vector vecb such that vecaxxvecb=vecc and veca.vecb = 3 where veca = hati + hatj+hatk , vecc = hatj-hatk

SHARAM PUBLICATION-QUESTION PAPER 2019-EXERCISE
  1. Evaluate : int0^(pi//2)(cosxdx)/((2-sinx)(3+sinx))

    Text Solution

    |

  2. Find the area of the region bounded by the curve y=6x-x^2 and the x-ax...

    Text Solution

    |

  3. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

    Text Solution

    |

  4. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

    Text Solution

    |

  5. Find a unit vector perpendicular to both of the vectors veca + vecb an...

    Text Solution

    |

  6. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

    Text Solution

    |

  7. Find the vector equation of a plane which is at a distance of 3 units ...

    Text Solution

    |

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

    Text Solution

    |

  9. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

    Text Solution

    |

  10. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

    Text Solution

    |

  11. Solve y^(2)+x^(2)dy/dx=xydy/dx.

    Text Solution

    |

  12. Evaluate the following integrals int(dx)/(2cos^2x+3cosx)

    Text Solution

    |

  13. Show by vector method that the four points (6, 2, -1), (2, -1, 3), (-1...

    Text Solution

    |

  14. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

    Text Solution

    |

  15. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

    Text Solution

    |

  16. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

    Text Solution

    |

  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

  18. Examining consistency and solvability, solve the following equation by...

    Text Solution

    |

  19. Out of the adult population in a village 50% are farmers, 30% do busin...

    Text Solution

    |

  20. Find the inverse of the following matrix using elementary transformati...

    Text Solution

    |