Home
Class 12
MATHS
Find the angles of /\ABC whose vertices ...

Find the angles of `/_\ABC` whose vertices are `A(-1,3,2), B(2,3,5) and C(3,5,-2)`.

A

`45^@`

B

`60^@`

C

`90^@`

D

`30^@`

Text Solution

Verified by Experts

The correct Answer is:
C
Now DR's of AB = (2+1,3-3,5-2) = (3,0,3) and AC = (3+1,5-3,-2-2) = (4,2,-4)
`thereforecosA=(3xx4+0xx2+3xx-4)/(sqrt(3^2+0+3^2)sqrt(4^2+2^2+(-4)^2))=(12-12)/(sqrt(36)sqrt(36))=0`
`rArr" "angleA=90^@`
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

  • STRAIGHT LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2(MISCELLANEOUS PROBLEMS)|30 Videos

  • TRIGONOMETRIC FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|26 Videos

Similar Questions

Explore conceptually related problems

Using vectors,find the area of the /_ABC, whose vertices are A(1,2,3),B(2,-1,4) and C(4,5,-1)

Find the angles of a triangle whose verties are A(3,2,1), B(35,2) and C(5,-2,3) .

Find the angles of a triangle whose vertices are A(0,-1,-2),B(3,1,4) and C(5,7,1)

Using vectors, find the area of Delta ABC whose vertices are (i) A(1,1,2),B(2,3,5) and C(1,5,5) (ii) A(1,2,3),B(2,-1,4) and C(4,5,-1) (iii) A(3,-1,2),B(1,-1,-3) and C(4,-3,1) (iv) A ( 1,-1,2),B(2,1,-1) and C(3,-1,2).

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

Using integration, find the area of the triangle ABC whose vertices are A(-1,1), B(0,5) and C(3,2) .

Find the angles of a triangle whose vertices are A(0,-1,-2),B(3,1,4)and C(5,7,1)

Find the area of Delta ABC whose vertices are : (i) A(1, 2), B (-2, 3) and C(-3, -4) (ii) A(-5, 7), B(-4, -5) and C(4, 5) (iii) A(3, 8), B(-4, 2) and C(5, -1) (iv) A(10, -6), B(2, 5) and C(-1, 3)

Find the area of triangle ABC whose vertices are A(-3, -5), B(5,2) and C(-9,-3).

Find the area of Delta ABC whose vertices are A(2, 7), B(3, -1) and C(-5, 6).

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-THREE DIMENSIONAL GEOMETRY-Exercise 2 (MISCELLANEOUS PROBLEMS)
  1. Find the angles of /\ABC whose vertices are A(-1,3,2), B(2,3,5) and C(...

    Text Solution

    |

  2. If projection of a line on X,Y and Z-axes are 6,2 and 3 respectively t...

    Text Solution

    |

  3. If OA is equally inclined to OX,OY ,OZ and if A is sqrt(3) units from ...

    Text Solution

    |

  4. If P(0,1,2),Q(4,-2,1) and O(0,0,0) are three points, then /POQ=

    Text Solution

    |

  5. A line makes the same angle theta with each of the x and z-axes. If t...

    Text Solution

    |

  6. If the directions cosines of a vector of magnitude 3 are (2/3,(-a)/3,2...

    Text Solution

    |

  7. If 1/2,1/3,n are direction cosines of a line, then the value of n is

    Text Solution

    |

  8. A line makes an angle theta both with x-axis and y-axis. A possible ra...

    Text Solution

    |

  9. The direction cosines to two lines at right angles are (1,2,3) and (-2...

    Text Solution

    |

  10. A line makes acute angles of alpha,beta and gamma with the coordinate ...

    Text Solution

    |

  11. The direction rations of the diagonals of a cube which joins the origi...

    Text Solution

    |

  12. The projection of the line segment joining (2,5,6) and (3,2,7) on the ...

    Text Solution

    |

  13. In DeltaABC the mid points of the sides AB, BC and CA are (l, 0, 0),...

    Text Solution

    |

  14. The diection cosines of two lines are proportional to (2,3,-6) and (3,...

    Text Solution

    |

  15. The angle between the lines whose direction cosines are (sqrt3/4,1/4,s...

    Text Solution

    |

  16. Let O be the origin and P be the point at a distance 3 units from orig...

    Text Solution

    |

  17. If the points A(2,3,-4), B(1,-2,3) and C(3,lambda,-1) are colliner, th...

    Text Solution

    |

  18. If the directions cosines of a straight line are ltk,k,kgt then

    Text Solution

    |

  19. Find the angle between the following pair of lines: A lines with direc...

    Text Solution

    |

  20. If P(p), Q(q), R(r) and S(s) be four points such that 3p+8q=6r+5s then...

    Text Solution

    |