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.

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

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

Two forces vec A B and vec A D are acting at vertex A of a quadrilateral ABCD and two forces vec C B and vec C D at C prove that their resultant is given by 4 vec E F , where E and F are the midpoints of AC and BD, respectively.

ABCDE is a pentagon .prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j such that vecalpha= vec a+ vec b+ vec c Then the resolution of the vector vecalpha into components with respect to vec aa n d vec b is given by a. 3 vec a-2 vec b b. 3 vec b-2 vec a c. 2 vec a-3 vec b d. vec a-2 vec b

If A B C D is a rhombus whose diagonals cut at the origin O , then proved that vec O A+ vec O B+ vec O C+ vec O D+ vec Odot

If A B C D is a rhombus whose diagonals cut at the origin O , then proved that vec O A+ vec O B+ vec O C+ vec O D+ vec Odot

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

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