Solve for `vec x`, the equation: ,br>`vec AE + vec x= vec AC`

Solve for vec x , the equation: vec DE + vec x = vec DC

Solve for vec x , the equation: vec AC+ vec x= vec 0

Solve for vec x , the equation: vec BE + vec x + vec ED = vec BD , where ABCD is a quadilateral whose diagonals intersects in E.

Solve the vector equation vec r xx vec a + k vec r = vec b , where vec a, vec b are two non-collinear vectors and k is any scalar.

If vec A=(1,1,1) , vec C=(0,1,-1) are two given vectors, then find a vector vec B satisfying the equations vec A xx vec B=vec C and vec A * vec B=3 .

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""X vec c"" =vec b""X vec d""=""a n d"" vec adot vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

If vec a,vec b,vec c are unit vectors such that vec a+vec b+ vec c= vec 0 , then the value of vec a *vec b +vec b* vec c+ vec c*vec a is equal to

If vec r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for some non-zero vector vec r , then the value of vec a*(vec b xx vec c) is........

If ABCD is a parallelogram and vec AB = vec a , vec BC= vec b then show that vec AC = vec a+ vec b and vec BD = vec b- vec a .

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p