Home
Class 12
MATHS
If vec x and vec y are two non-collinea...

If ` vec x and 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 xx vec y)=0,` then ` A B C` is (where ` vec x` X `vec y` is perpendicular to the plane of `x and y` ) 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.
Promotional Banner

Similar Questions

Explore conceptually related problems

(vec b xx vec c) xx (vec c xx vec a ) =

If vec a xx vec b = vec c and vec b xx vec c = vec a then

vec a .[(vec b + vec c) xx (vec a + vec b + vec c)] =

If vec(a) is vector perpendicular to both vec(b) and vec(c ) , then

[vec a + vec b vec b + vec c vec c + vec a] =

If vec a, vec b, vec c are non-coplanar vectors and lambda is a real number, then [lambda ( vec a + vec b) lambda^(2) vec b lambda vec c] = [ vec a vec b + vec c vec b] for

If vec a = j-k and vec c = i-j-k . Then the vector vec b satisfying vec a xx vec b + vec c = vec 0 and vec a. vec b = 3 is

If vec a and vec b are unit vectors |vec a xx vec b| =1 then the angle between vec a and vec b is