If ` vec (a), vec(b) and vec ( c) ` are three vectors of magnitude 3,4 and 5 respectively such that each vector is perpendicular to the sum of the other two vectors , prove that ` | vec (a) + vec(b) + vec (c ) | = 5 sqrt (2)`

(d) answer any one question : (i) if three vectors vec a, vec b and vec c of magnitudes 3,4and5 are such that each vector is perpendicular to the sum of the other two vectors,then prove that |vec a+ vec b+vec c|= 5 sqrt 2 .

Three vectors veca, vecb, vec c are such that |veca|=3, |vecb|=2, |vec c|=6 , if each vector is perpendicular to the sum of the other two vectors, then the value of |veca+vecb+vec c| is -

If vec(a) , vec(b)and vec(a) xx vec(b) are three unit vectors , find the angles beween the vectors vec(a) and vec(b)

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 )

vec a , vec b , and vec c are three vectors of equal magnitude. The angle between each pair of vectors is pi//3 such that | vec a+ vec b+ vec c|=sqrt6. Then | vec a| is equal to a. 2 b. -1 c. 1 d. sqrt(6)//3

Show that the vector vec(a) is perpendicular to the vector vec(b) - (vec(a).vec(b))/(|vec(a)|^(2))vec(a)

If vec(a) , vec(b) and vec (c ) are three unit vectors such that vec(a).vec(b) = vec(a).vec (c )=0 and angle between vec(b) and vec (c ) is pi/6 , prove that , vec (a) = pm 2 ( vec(b) xx vec(c ))

If vec a and vec b are any two vectors of magnitudes 2 and 3, respectively, such that |2( vec axx vec b)|+|3( vec a. vec b)|=k , then the maximum value of k is a. sqrt(13) b. 2sqrt(13) c. 6sqrt(13) d. 10sqrt(13)

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

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 dot