Home
Class 12
MATHS
Statement 1 : In DeltaABC, vec(AB) + vec...

Statement 1 : In `DeltaABC`, `vec(AB) + vec(BC) + vec(CA) = 0`
Statement 2 : If `vec(OA) = veca, vec(OB) = vecb`, then `vec(AB) = veca + vecb`

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

In `DeltaABC,AB+BC=AC=-CA`
or `AB+BC+CA=0`
OA+AB=OB is the triangle law of addition.
Hence, statement 1 is true and statement 2 is false.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|11 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|1 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If vec a * vec a=0 then vec a is a

If vec(a).vec(b)=0 and vec(a) xx vec(b)=0, " prove that " vec(a)= vec(0) or vec(b)=vec(0) .

Knowledge Check

  • If ABCDEF is a regular hexagon with vec(AB) = vec(a) ,vec(BC ) = vec(b) then vec(CE) equals :

    A
    `vec(b) - vec(a)`
    B
    `- vec(b)`
    C
    `vec(b) - 2vec(a)`
    D
    `vec(b) +2vec(a)`
  • Similar Questions

    Explore conceptually related problems

    Given a parallelogram ABCD . If |vec(AB)|=a, |vec(AD)| = b & |vec(AC)| = c , then vec(DB) . vec(AB) has the value

    Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

    If vec a+ vec b + vec c= 0 , show that vec axxvec b= vec bxx vec c= vec cxx vec a .

    Orthocenter of an equilateral triangle ABC is the origin O. If vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc , then vec(AB)+2vec(BC)+3vec(CA)=

    In a triangle OAC, if B is the mid point of side AC and vec(OA)=veca,vec(OB)=vecb , then what is vec(OC) .

    Let A and B be points with position vectors veca and vecb with respect to origin O . If the point C on OA is such that 2vec(AC)=vec(CO), vec(CD) is parallel to vec(OB) and |vec(CD)|=3|vec(OB)| then vec(AD) is (A) vecb-veca/9 (B) 3vecb-veca/3 (C) vecb-veca/3 (D) vecb+veca/3

    If ABCD is a parallelogram and vec AB = vec a , vec BC= vec b then show that vec AC = vec a+ vec b and vec BD = vec b- vec a .