If `vec a` is a unit vector and `(vec x - vec a).(vec x + vec a) = 8`, then find `|vec x|`.

Find |vec x| , if for a unit vector vec a, (vec x - vec a)(vec x + vec a) = 12 .

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c dot vec b

Let vec a , vec b , vec c be three unit vectors and vec a . vec b= vec a . vec c=0. If the angel between vec b and vec c is pi/3 , then find the value of |[ vec a vec b vec c]| .

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=3a n d| vec b|=2. Then vec r=2/3( vec a+ vec axx vec b) b. vec r=1/3( vec a+ vec axx vec b c. vec r=2/3( vec a- vec axx vec b d. vec r=1/3(- vec a+ vec axx vec b

Find |vec a| and |vec b| if (vec a + vec b).(vec a - vec b) = 3 and 2|vec b| = |vec a| .

If vec a , vec ba n d vec c are three non-zero vectors, no two of which ar collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c|dot

(i) Write the scalar componets of 3 hat i - 2 hat j + 5 hat k . (ii) Find the angle between the vectors hat i + hat j and hat i - hat j . (iii) Find |vec x| , if veca is a unit and (vec x + vec a) .(vec x - vec a) = 0 .

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

If vec a , vec b ,a n d vec c are there mutually perpendicular unit vectors and vec d is a unit vector which makes equal angles with vec a , vec b ,a n d vec c , the find the value off | vec a+ vec b+ vec c+ vec d|^2dot