Home
Class 12
MATHS
If vec x and vec y are two non-collinear...

If `vec x` and `vec y` are two non-collinear vectors and ABC is a triangle with side lengths a,b and c satisfying (20a-15b)`vec x` + (15b-12c)`vec y` + (12c-20a)`vec x xx vec y` is:

A

an acute angled Delta

B

an obtuse angled Delta

C

a right angled Delta

D

an isosceles Delta

Text Solution

Verified by Experts

The correct Answer is:
3
`(20a-15b)overset(rarr)x,overset(rarr)y "and" overset(rarrxxxoverset(rarr)y) "are linearly independent"`
`rArr 20a-15b =15b -12c=12a-12a=0`
`rArrc^(2)=a^(2)+b^(2)`
"hence , Delta ABC is right angled"
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 8

    CAREER POINT|Exercise PART (C ) - MATHS|30 Videos

Similar Questions

Explore conceptually related problems

If vec x and vec y are two non-collinear vectors and ABC is a triangle with side lengths a,b and c satisfying (20a-15b)vec x+(15b-12c)vec y+(12c- 20a) vec x xxvec y is:

If vec x and vec y are two non-collinear vectors and ABC isa triangle with side lengths a,b, and satisfying (20a-15b)vec x+(15b-12c)vec y+(12c-20a)(vec xxvec y)=0 then triangle ABC is a.an acute-angled triangle b.an obtuse- angled triangle c.a right-angled triangle d.an isosceles triangle

If vec x andvec y are two non-collinear vectors and a triangle ABC with side lengths a,b,c satisfying (20a-15b)vec x+(15b-12c)vec y+(12c-20a)(vec x xx vec y) = vec0 . Then triangle ABC is:

If vec xa n d vec y are two non-collinear vectors and a, b, and c represent the sides of a A B C satisfying (a-b) vec x+(b-c) vec y+(c-a)( vec xxx vec y)=0, then A B C is (where vec xxx vec y is perpendicular to the plane of xa n dy ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle

vec a and vec b are two non-collinear unit vectors vec a,vec b,xvec a-yvec b form a triangle.

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If vec b and vec c be any two non-collinear vectors,and vec a be any vector then (vec a*vec b)vec b+(vec a*vec c)vec c+(vec a*(vec b xxvec c))/(|vec b xxvec c|^(2))(vec b xxvec c) is equal to

If vec b and vec c be any two non-collinear vectors,and vec a be any vector then (vec a*vec b)vec b+(vec a*vec c)vec c+(vec a*(vec b xxvec c))/(|vec b xxvec c|^(2))(vec b xxvec c) is equal to

If vec b and vec c are two non-collinear vectors such that vec a*(vec b+vec c)=4 and vec a xx(vec b xxvec c)=(x^(2)-2x+6)vec b+(sin y)vec c then the point (x,y) lies on

If vec a and vec b are non-collinear vectors,find the value of x for which the vectors vec alpha=(2x+1)vec a-vec b and vec beta=(x-2)vec a+vec b are collinear.

CAREER POINT-MOCK TEST 9-MATHS
  1. OAB is a triangle in the horizontal plane through the foot P of the...

    Text Solution

    |

  2. If vec x and vec y are two non-collinear vectors and ABC is a triangle...

    Text Solution

    |

  3. If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,...

    Text Solution

    |

  4. The equation of the plane passing through the lines (x-4)/(1)=(y-3)/(1...

    Text Solution

    |

  5. The Delta with vertices (x(i),y(i)) i=1,2,3 "is inscribed in the circl...

    Text Solution

    |

  6. If the line px + qy =1 is a tangent to the parabola y^(2) =4ax, then

    Text Solution

    |

  7. If int (2tan x+3)/(sin^(2)x+2cos^(2)x)dx =1(n)(1+sec^(2)x)+ p tan^(-...

    Text Solution

    |

  8. If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing ...

    Text Solution

    |

  9. If f(x) is continuous and increasing functin such that the domain of g...

    Text Solution

    |

  10. If f(x)={alpha+sin[x]/x , x > 0 and 2 ,x=0 and beta+[(sin x-x)/x^3] ,x...

    Text Solution

    |

  11. Find the greatest value of the term independent of x in the expansion ...

    Text Solution

    |

  12. The polynomial f(x)=x^4+a x^3+b x^3+c x+d has real coefficients and f(...

    Text Solution

    |

  13. If b^(2) -ac lt 0 and a gt 0 then the value of the determinant is

    Text Solution

    |

  14. The probability that sin^(-1)(sin x)+cos^(-1)(cos y) is an integer x, ...

    Text Solution

    |

  15. If the points P(alpha,0) and Q(0,beta) always lies inside sthe Delta f...

    Text Solution

    |

  16. The equation of the hyperbola whose foci are (6.5), (-4,5) and eccentr...

    Text Solution

    |

  17. The value of the definite integral int(0)^(3pi//4)(1+x)sin x+(1-x) cos...

    Text Solution

    |

  18. The value of the constant 'm' and 'c' for which y = mx + c is a soluti...

    Text Solution

    |

  19. Through the centriod of an equilateral triangle a line parallel to the...

    Text Solution

    |

  20. If the number of ways of selecting 3 numbers out of 1, 2, 3, ……., 2n+1...

    Text Solution

    |