The non-zero vectors `vec a` , `vec b` and `vec c` are related by `vec a=8 vec b` and `vec c = −7 vec b`, then the angle between `vec a` and `vec c` is

If vec a and vec b are non - zero vectors and |vec a+ vec b| = |vec a - vec b| , then the angle between vec a and vec b is

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then (a) vec a , vec b ,a n d vec c can be coplanar (b) vec a , vec b ,a n d vec c must be coplanar (c) vec a , vec b ,a n d vec c cannot be coplanar (d)none of these

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

Show that the vectors vec a, vec b and vec c are coplanar if vec a + vec b, vec b + vec c, vec c+ vec a are coplanar.

Let vec r be a non-zero vector satisfying vec r . vec a= vec r . vec b= vec r . vec c=0 for given non-zero vectors vec a , vec ba n d vec cdot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , angle, between vec aa n d vec b is (2pi)/3,| vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angel between vec aa n d vec b is a. pi/6 b. pi/4 c. pi/3 d. pi/2

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0