Home
Class 12
MATHS
Let the vectors PQ, QR, RS, ST, TU and U...

Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a regular hexagon.
Statement-I `PQxx(RS+ST)ne0`, becouse
Statement-II `PQtimesRS=0 and PQtimesSTne0`

A

Both Statement-I and Statement-II are correct and Statement-II is the correct explanation of Statement-I

B

Both Statement-I and Statement-II are correct but Statement-II is not the correct explanation of Statement-I

C

Statement-I is correct but Statement-II is incorrect

D

Statement-II is correct but Statement-I is incorrect

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|18 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

Let the vectors PQ,OR,RS,ST,TU and UP represent the sides of a regular hexagon. Statement I: PQxx(RS+ST)ne0 Statement II: PQxxRS=0 and PQxxSTne0

Let the vectors vec(PQ),vec(QR),vec(RS), vec(ST), vec(TU) and vec(UP) represent the sides of a regular hexagon. Statement I: vec(PQ) xx (vec(RS) + vec(ST)) ne vec0 Statement II: vec(PQ) xx vec(RS) = vec0 and vec(PQ) xx vec(RS) = vec0 and vec(PQ) xx vec(ST) ne vec0 For the following question, choose the correct answer from the codes (A), (B) , (C) and (D) defined as follows:

Given : A circle, 2x^2+""2y^2=""5 and a parabola, y^2=""4sqrt(5)""x . Statement - I : An equation of a common tangent to these curves is y="x+"sqrt(5) Statement - II : If the line, y=m x+(sqrt(5))/m(m!=0) is their common tangent, then m satisfies m^4-3m^2+""2""=0. (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I (2) Statement -I is True; Statement -II is False. (3) Statement -I is False; Statement -II is True (4) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Statement-I int_0^9[sqrtx]dx=13, Statement-II int_0^(n^2) [sqrt x]dx=(n(n-1)(4n+1))/6, n in N (where [.] denotes greatest integer function) (1) Statement-I is true, Statement-II is true Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true Statement-II is not a correct explanation for Statement-I, (3) Statement-I is true, Statement-II is false. (4) Statment-I is false, Statement-II is true.

Statement-1: If the equations ax^2 + bx + c = 0 (a, b, c in R and a != 0) and 2x^2 + 7x+10=0 have a common root, then (2a+c)/b =2. Statement-2: If both roots of a_1 x^2 + b_1 x+c_1 = 0 and a_2 x^2 + b_2x + c_2 = 0 are same, then a_1/a_2=b_1/b_2=c_1/c_2. Given a_1,b_1,c_1,a_2,b_2,c_2 in R and a_1 a_2 != 0. (i) Statement I is true , Statement II is also true and Statement II is correct explanation of Statement I (ii)Statement I is true , Statement II is also true and Statement II is not correct explanation of Statement I (iii) Statement I is true , Statement II is False (iv) Statement I is False, Statement II is True

For the following question, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows: Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I. Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I. Statement I is true; Statement II is false Statement I is false; Statement II is true. Let a , b , c , p , q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0 and alpha,1/beta are the roots of the equation a x^2+2b x+c=0, where beta^2 !in {-1,0,1}dot Statement I (p^2-q)(b^2-a c)geq0 and Statement II b !in p a or c !in q adot

Statement I is True: Statement II is True; Statement II is a correct explanation for statement I Statement I is true, Statement II is true; Statement II not a correct explanation for statement I. Statement I is true, statement II is false Statement I is false, statement II is true Let f: R->R [0,\ pi//2] defined by f(x)=tan^(-1)(x^2+x+a) , then Statement I: The set of values of a for which f(x) is onto is [1/4,oo) because Statement II: Minimum value of x^2+x+a\ i s\ a-1/4dot a. A b. \ B c. \ C d. D

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The edges of a parallelopiped are of unit length and are parallel to ...

    Text Solution

    |

  2. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |

  3. Let the vectors PQ, QR, RS, ST, TU and UP represent the sides of a reg...

    Text Solution

    |

  4. The number of distinct real values of lambda, for which the vectors -l...

    Text Solution

    |

  5. Let veca,vecb,vecc be unit vectors such that veca+vecb+vecc=vec0. Whic...

    Text Solution

    |

  6. Let A be vector parallel to line of intersection of planes P1 and P2. ...

    Text Solution

    |

  7. Let a=hat(i)+2hat(j)+hat(k), b=hat(i)-hat(j)+hat(k), c=hat(i)+hat(j)-h...

    Text Solution

    |

  8. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

    Text Solution

    |

  9. The unit vector which is orthogonal to the vector 3hati+2hatj+6hatk an...

    Text Solution

    |

  10. The value of a so that the volume of parallelepiped formed by hat ...

    Text Solution

    |

  11. If vec a=( hat i+ hat j+ hat k), vec adot vec b=1a n d vec axx vec b=...

    Text Solution

    |

  12. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

    Text Solution

    |

  13. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

    Text Solution

    |

  14. Let a= 2hat(i) -2hat(k) , b=hat(i) +hat(j) and c be a vectors suc...

    Text Solution

    |

  15. If [axxb bxxc c xxa]=lambda[abc]^(2), then lambda is euqual to

    Text Solution

    |

  16. Let hata and hatb be two unit vectors. If the vectors vecc=hata+2hatb ...

    Text Solution

    |

  17. Let ABCD be a parallelogram such that vec AB = vec q,vec AD = vec p a...

    Text Solution

    |

  18. 1/sqrt(10)(3hatj + hatk) and vecb =(2hati +3hatj-6hatk), then the valu...

    Text Solution

    |

  19. The vectors a and b are not perpendicular and c and d are two vectors ...

    Text Solution

    |

  20. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

    Text Solution

    |