Home
Class 12
MATHS
Statement 1: In "Delta"A B C , vec A B+ ...

Statement 1: In `"Delta"A B C , vec A B+ vec A B+ vec C A=0` Statement 2: If ` vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b`

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
C

In `Delta ABC`,` vec(AB) + vec(BC) = vec(AC) =- vec(CA)`
or `" " vec(AB) + vec(BC) + vec(CA) = vecO`
`vec(OA) + vec(AB) = vec(OB)` is the triangle law of addition.
Hence statement 1 is true and Statement 2 is false.
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|11 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise MATRIX-MATCH TYPE|3 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|13 Videos
  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|541 Videos

Similar Questions

Explore conceptually related problems

Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 Statement 2: If vec (O A)= vec a , vec (O B)= vec b ,t h e n \ vec (A B)= vec a+ vec b

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdot vec b= vec rdot vec c=0 for given non-zero vectors vec a , vec b and vec c dot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

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

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .