If `vec(c )=vec(a)-vec(b)`, which of the following relations among magnitudes cannot be achieved by any choice of `vec(a)` and `vec(b)` ?

If vec(a), vec(b),vec(c ) are any vectors, then which the following is equal to vec(a) xx vec(b) +vec(b)xx vec(c ) + vec(c ) xx vec(a) ?

If vec(a) , vec (b) and vec (c ) are three mutually perpendicular vectors of equal magnitude , show that , vectors vec (a) , vec (b) , vec (c ) make an equal angle with vec(a) + vec (b) + vec (c )

Give vec A + vec B+ vec C + vec D =0 , which of the following statements are correct ? (a) vec A, vec B ,vec C abd vec C must each be a null vector. (b) The magnitude of ( vec A + vec C) equals the magnitude of ( vec B + vec D0 . ltBrgt (c ) The magnitude of vec A can never be greater than the sum of the magnitude of vec B , vec C and vec D . ( d) vec B + vec C must lie in the plance of vec A + vec D. if vec A and vec D are not colliner and in the line of vec A and vec D , if they are collinear.

If vec x+ vec cxx vec y= vec a and vec y+ vec cxx vec x= vec b ,where vec c is a nonzero vector, then which of the following is not correct? a. vec x=( vec bxx vec c+ vec a+( vec c . vec a) vec c)/(1+ vec c . vec c) b. vec x=( vec cxx vec b+ vec b+( vec c . vec a) vec c)/(1+ vec c . vec c) c. vec y=( vec axx vec c+ vec b+( vec c . vec b) vec c)/(1+ vec c . vec c) d. none of these

If vec(a)xx vec(b) = vec(c) and vec(b) xx vec(c) = vec(a) , then which one of the following is correct?

If vec a,vec b, and vec c are mutually perpendicular vectors of equal magnitudes,then find the angle between vectors vec a and vec a+vec b+vec c

If vec(a),vec(b),vec( c ) are mutually perpendicular vectors of equal magnitudes, show that the vector vec(a)+vec(b)+vec( c ) is equally inclined to vec(a),vec(b) and vec( c ) .