Home
Class 12
MATHS
If a plane cuts off intercepts OA = a, ...

If a plane cuts off intercepts `OA = a, OB = b, OC = c` from the coordinate axes 9where `'O'` is the origin). then the area of the triangle `ABC` is equal to

A

`(1)/(2)(ab+bc+ac)`

B

`(1)/(2)abc`

C

`(1)/(2)(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2))^(1//2)`

D

`(1)/(2)(a+b+c)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
c
Plane meets axes at A(a,0,0), B(0,b,0) and C(0,0,c), Then area of `DeltaABC`
`=(1)/(2)|vec(AB)xxvec(AC)|`
`=(1)/(2)|(-ahati+bhatj)xx(-ahati+chatk)|`
`=(1)/(2)sqrt(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2))`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|17 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise REASONING TYPE|10 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise SUBJECTIVE TYPE|17 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

If Delta =a^(2) -(b-c) ^(2), where Delta is the area of the triangle ABC, then tan A is equal to-

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is-

A line is drawn through the point ( 1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

If the tangent to the curve 2y^3=ax^2+x^3 at the point (a,a) cuts off Intercepts alpha and beta on the coordinate axes, (where alpha^2+beta^2=61) then the value of a is

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

A straight line passing through P(3,1) meets the coordinate axes at Aa n dB . It is given that the distance of this straight line from the origin O is maximum. The area of triangle O A B is equal to

Through the point P( alpha, beta ,lambda) a plane is drown prependicular to OP where O is the origin. Let this plane meet the coordinate axes at L,M and N .Show that the area of the triangle LMN =r^(5)/((2 alpha beta lambda)) where |vec(OP)|=r

Let (h,k) be a fixed point where hgt0,kgt0 . A straight line passing through this point cuts the positive directions of the coordinate axes at the points P and Q . Find the minimum area of the triangle OPQ , O being the origin.

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at Aa n dB , then the maximum area of the triangle O A B , where O is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

A plane meets the coordinates axes in A, B, C such that the centroid of the triangle ABC is the point (a,a,a) .Then the equation of the plane is x+y+z=p , where p is ___

CENGAGE PUBLICATION-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
  1. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

    Text Solution

    |

  2. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+z...

    Text Solution

    |

  3. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

    Text Solution

    |

  4. A line makes an angel theta with each of the x-and z-axes. If the a...

    Text Solution

    |

  5. The shortest distance from the plane 12 x+y+3z=327 to the sphere x^...

    Text Solution

    |

  6. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

    Text Solution

    |

  7. The radius of the circle in which the sphere x^(2)+y^(2)+z^(2)+2x-2y-4...

    Text Solution

    |

  8. The lines (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k=(y-4)/2=(z-5)/1 are c...

    Text Solution

    |

  9. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

    Text Solution

    |

  10. Two systems of rectangular axes have the same origin. If a plane cu...

    Text Solution

    |

  11. The plane, which passes throught the point (3,2,0) and line (x - 3)/1 ...

    Text Solution

    |

  12. The direction ratios of a normal to the plane through (1,0,0)a n d(...

    Text Solution

    |

  13. The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15...

    Text Solution

    |

  14. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

    Text Solution

    |

  15. Distance of the point P( vec p) from the line vec r= vec a+lambda vec...

    Text Solution

    |

  16. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

    Text Solution

    |

  17. The plane vec rdot vec n=q will contain the line vec r= vec a+lambda...

    Text Solution

    |

  18. The projection of point P( vec p) on the plane vec r. vec n=q is ( v...

    Text Solution

    |

  19. The angle between i and line of the intersection of the plane vec r ....

    Text Solution

    |

  20. The line (x+6)/5=(y+10)/3=(z+14)/8 is the hypotenuse of an isosceles ...

    Text Solution

    |