In ` A B C` Prove that `A B^2+A C^2=2(A O^2+B O^2)` , where `O` is the middle point of `B C`

Prove that the resultant of two forces acting at point O and represented by vec O B and vec O C is given by 2 vec O D ,where D is the midpoint of BC.

In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

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

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.

Statement 1 :If the lines 2x+3y+19=0 and 9x+6y-17=0 cut the x-axis at A ,B and the y-axis at C ,D , then the points, A , B , C , D are concyclic. Statement 2 : Since O A x O B=O C x O D , where O is the origin, A , B , C , D are concyclic.

The base of the pyramid A O B C is an equilateral triangle O B C with each side equal to 4sqrt(2),O is the origin of reference, A O is perpendicualar to the plane of O B C and | vec A O|=2. Then find the cosine of the angle between the skew straight lines, one passing though A and the midpoint of O Ba n d the other passing through O and the mid point of B Cdot

In Delta ABC, prove that (a^(2) - b^(2) + c^(2)) tan B = (a^(2) + b^(2) - c^(2)) tan C.

If A + B + C = 180^(@) , prove that sin^(2)A + sin^(2)B + sin^(2) C = 2 + 2 cos A cos B cos C

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.