If ` vec xa n d vec y` are two non-collinear vectors and `A B C` isa triangle with side lengths `a ,b ,a n dc` satisfying `(20 a-15 b) vec x+(15b-12 c) vec y+(12 c-20 a)( vecx xx vec y)=0,` then triangle `A B C` is
a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. an isosceles triangle

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 xx vec y)=0, then A B C is (where vec xxx 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

The points (0,8/3),(1,3) and (82 ,30) are the vertices of (A) an obtuse-angled triangle (B) an acute-angled triangle (C) a right-angled triangle (D) none of these

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

The points (-a ,-b),(a , b),(a^2,a b) are (a) vertices of an equilateral triangle (b) vertices of a right angled triangle (c) vertices of an isosceles triangle (d) collinear

If all the vertices of a triangle have integral coordinates, then the triangle may be (a) right-angle (b) equilateral (c) isosceles (d) none of these

The points (a , b),(c , d), and ((k c+l a)/(k+l),(k d+l b)/(k+l)) are (a) vertices of an equilateral triangle (b) vertices of an isosceles triangle (c) vertices of a right-angled triangle (d) collinear

If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right angled (b) obtuse angled (c)isosceles (d) equilateral

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 and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]