Is ` |vec A - vec B|` greater than or less than ` |vec A| + |vec B|` ? Explain.

Is | vec A + vec B| greater than or less than |vec A| + |vec B| ? Explain.

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 a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

Given vec A+ vec B+ vec + vec D=0 , can the magnitude of vec A + vec B + vec C be equal to the magnitude of vec D Explain.

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

If vec a, vec b and vec c are perpendicular to vec b + vec c, vec c + vec a, vec a + vec b respectively and if | vec a + vec b | = 6, | vec b + vec c | = 8 and | vec c + vec a | = 10 then find the value of vec a + vec b + vec c

If vec a + vec b = vec c and | vec a | = | vec b | = | vec c | find the angle between vec a and vec b

Three vectors vec a, vec b and vec c satisfy the condition vec a + vec b + vec b + vec c = vec 0 .Evaluate the quantity mu = vec a * vec b + vec b * vec c + vec c * vec a , if | vec a | = 1 | vec b | = 4 and | vec c | = 2

Given four vectors vec a, vec b, vec c, vec d such that vec a + vec b + vec c = alphavec d, vec b + vec c + vec d = betavec a and that vec a, vec a, vec b, vec c are non-coplanar, then the sum vec a + vec b + vec c + vec d is