If `axx(bxxc)=(axxb)xxc ,` then `( vec cxx vec a)xx vec b= vec0` b.` vec cxx( vec axx vec b)= vec0` c. ` vec bxx( vec cxx vec a) =0` d. `( vec cxx vec a)xx vec b= vec bxx( vec cxx vec a)= vec0`

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

Let the pairs a , b,and c ,d each determine a plane. Then the planes are parallel if a. ( vec axx vec c)xx( vec bxx vec d)= vec0 b. ( vec axx vec c).( vec bxx vec d)= vec0 c. ( vec axx vec b)xx( vec cxx vec d)= vec0 d. ( vec axx vec b).( vec cxx vec d)= vec0

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

For any three vectors veca , vec b , vec c show that vecaxx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)= vec0

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

If vec a , vec b , and vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c| .