If the position vectors of the points `A(3,4),B(5,-6)` and `(4,-1)` are ` vec a , vec b , vec c` respectively compute ` vec a+2 vec b-3 vec c `

If the position vectors of the points A(3,4),B(5,-6) and C (4,-1) are vec a , vec b , vec c respectively compute vec a+2 vec b-3 vec c

The position vectors of A, B,C and D are vec a , vec b , vec 2a+ vec 3b and vec a - vec 2b respectively show that vec DB=3 vec b -vec a and vec AC =vec a + vec 3b

vec a , vec b and vec c are the position vectors of points A ,B and C respectively, prove that : vec a× vec b+ vec b× vec c+ vec c× vec a is vector perpendicular to the plane of triangle A B Cdot

If the position vector of these points are vec(a) -2vec(b)+3 vec(c ), 2 vec(a)+3vec(b)-4 vec( c) ,-7 vec(b) + 10 vec(c ) , then the three points are

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are vec(a) , vec(b) , vec(c ) and (vec(a) + vec(b) + vec(c ))/(4) respectively, then the position vector of the orthocentre of this triangle is

Vectors drawn the origin O to the points A , B and C are respectively vec a , vec b and vec4a- vec3bdot find vec A C and vec B Cdot

If vec a ,\ vec b ,\ vec c are position vectors o the point A ,\ B ,\ a n d\ C respectively, write the value of vec A B+ vec B C+ vec A Cdot

P is a point on the line through the point A whose position vector is vec a and the line is parallel to the vector vec b . If P A=6, the position vector of P is: (a) vec a+6 vec b (b) vec a+6/(| vec b|) vec b (c) vec a-6 vec b/(| vec b|) (d) vec b+6/(| vec a|) vec a

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

If vec a , vec ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.