Home
Class 12
MATHS
Find the area of a triangle having verti...

Find the area of a triangle having vertices `A(3,2),B(11 ,8),` and `C(8,12)dot`

Text Solution

Verified by Experts

The area of triangle is
`A=(1)/(2)||underset(8" "12" "1)underset(11" "8" "1)(3" "2" "1)||`
Operating `R_(1) to R_(2) " and " R_(2) to R_(3) ` we get
`A=(1)/(2) ||underset(8" "12" "1)underset(3" "-4" "0)(-8" "-6" "0)||=(1)/(2)|underset(2" "-4)(-8" "-6)|=25 " sq. units"`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Find the area of the triangle with vertices A(1,1,2)B(2,3,5) and C(1,5,5).

Find the area of the triangle with vertices are(3,5)(2,4)(5,1).

Find the area of a triangle having the points A(1,0,0),B(0,1,0) and C(0,0,1) as its vertices.

Find the area of the triangle whose vertices are A (3,-1,2), B(1,-1,-3) and C(4,-3,1).

Find the area of the triangle whose vertices are (3,8) ,(-4,2) and ( 5,1 )

Find the area of the triangle whose vertices are (0,0), (1,2) and (4,3).

Find the area of atriangle having the points A(1,1,1), B (1,2,3) and C(2,3,1) as its vertices.

Find the area of the triangle whose vertices are A(3, -1,2) ,B(1, - 1, 3) and C(4, - 3 , 1)

Using vectors, find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).

CENGAGE-DETERMINANTS-All Questions
  1. Find the area of a triangle having vertices A(3,2),B(11 ,8), and C(8,1...

    Text Solution

    |

  2. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

    Text Solution

    |

  3. If f(theta)=|sinthetacosthetasintheta costhetasinthetacostheta costhet...

    Text Solution

    |

  4. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

    Text Solution

    |

  5. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

    Text Solution

    |

  6. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

    Text Solution

    |

  7. The determinant "Delta"=|(a^2+x) ab ac ab (b^2+x) bc ac bc (c^2+...

    Text Solution

    |

  8. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is d...

    Text Solution

    |

  9. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

    Text Solution

    |

  10. If (x)= |x^2+4x-3 2x+4 13 ...

    Text Solution

    |

  11. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

    Text Solution

    |

  12. Let f (n) = |{:(n,,n+1,,n+2),(.^(n)P(n),,.^(n+1)P(n+1),,.^(n+2)P(n+2)...

    Text Solution

    |

  13. If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e...

    Text Solution

    |

  14. Let x<1, then value of [[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]...

    Text Solution

    |

  15. If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|then

    Text Solution

    |

  16. Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are non...

    Text Solution

    |

  17. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

    Text Solution

    |

  18. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

    Text Solution

    |

  19. If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has com...

    Text Solution

    |

  20. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

    Text Solution

    |

  21. Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of ...

    Text Solution

    |