Home
Class 12
MATHS
If vec xa n d vec y are two non-colline...

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 x X vec y)=0,` then ` A B C` is (where ` vec x X 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

A

an acute angled triangle

B

ann obtuse angled triangle

C

a right angled triangle

D

a scalene triangle

Text Solution

Verified by Experts

The correct Answer is:
A
As x,y and `x xxy` are non-collinear vectors, vectors are linearly independent.
hence, `a-b=0=b-c=c-a`
or a=b=c
therefore, the triangle is equilateral.
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

If vec x and vec 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 the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

Knowledge Check

  • The vectors vec(a) and vec(b) are not perpendicular. The vectors vec( c ) and vec(d) are such that vec(b)xx vec( c )=vec(b)xx vec(d) and vec(a).vec(d)=0 then vec(d) = ……………

    A
    `vec( c )+((vec(a)*vec( c ))/(vec(a)*vec(b)))vec(b)`
    B
    `vec(b)+((vec(b)*vec( c ))/(vec(a)*vec(b)))vec( c )`
    C
    `c-((vec(a)*vec( c ))/(vec(a)*vec(b)))vec(b)`
    D
    `vec(b)-((vec(b)*vec( c ))/(vec(a)*vec(b)))vec( c )`

  • Let vec(a) and vec(b) be two unit vectors and theta is the angle between them. Then vec(a)+vec(b) is a unit vector if ……….

    A
    `theta=(pi)/(4)`
    B
    `theta=(pi)/(3)`
    C
    `theta=(pi)/(2)`
    D
    `theta=(2pi)/(3)`

    • Similar Questions

    Explore conceptually related problems

    If vec(a) and vec(b) are non-collinear vectors find the value of x for which vectors vec(alpha)=(x-2)vec(a)+vec(b) and vec(beta)=(3+2x)vec(a)-2vec(b) are collinear.

    The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

    The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

    vec(a) and vec(b) are unit vectors and angle between them is pi/k . If vec(a)+2vec(b) and 5vec(a)-4vec(b) are perpendicular to each other then find the integer value of k.

    If vec(A)xxvec(B)=vec(B)xxvec(A) , then the angle between vec(A) and vec(B) is-

    If G is the centroid of Delta ABC and G' is the centroid of Delta A' B' C' " then " vec(A A)' + vec(B B)' + vec(C C)' =

    Home
    Profile