If ` vec A O+ vec O B= vec B O+ vec O C` , then `A ,Bn a dC` are (where `O` is the origin) a. coplanar b. collinear c. non-collinear d. none of these

if vec Ao + vec O B = vec B O + vec O C ,than prove that B is the midpoint of AC.

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then (a) vec a , vec b ,a n d vec c can be coplanar (b) vec a , vec b ,a n d vec c must be coplanar (c) vec a , vec b ,a n d vec c cannot be coplanar (d)none of these

Let vec O A- vec a , vec O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC are non-collinear points. Let p denotes the areaof quadrilateral O A C B , and let q denote the area of parallelogram with O Aa n dO C as adjacent sides. If p=k q , then find kdot

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 vecd dot vec a= vecd dot vec b= vec d dot vec ca 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 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 vecd dot vec a= vecd dot vec b= vec d dot vec ca 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

If vec r . vec a= vec r . vec b= vec rdot vec c=1/2 or some nonzero vector vec r , then the area of the triangle whose vertices are A( vec a),B( vec b)a n dC( vec c)i s( vec a , vec b , vec c are non-coplanar ) a. |[ vec a vec b vec c]| b. | vec r| c. |[ vec a vec b vec c] vec r| d. none of these

Let vec a , vec b ,a n d vec c be non-zero vectors and vec V_1= vec axx( vec bxx vec c)a n d vec V_2( vec axx vec b)xx vec cdot Vectors vec V_1a n d vec V_2 are equal. Then vec aa n vec b are orthogonal b. vec aa n d vec c are collinear c. vec ba n d vec c are orthogonal d. vec b=lambda( vec axx vec c)w h e nlambda is a scalar

If 4 vec a+5 vec b+9 vec c=0, then ( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)] is equal to a. vector perpendicular to the plane of a ,b ,c b. a scalar quantity c. vec0 d. none of these

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these