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

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

Given vec a=x hat i+y hat j+2 hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j ; vec a_|_ vec b , vec adot vec c=4. Then [ vec a vec b vec c]^2=| vec a| b. [ vec a vec b vec c]^=| vec a| c. [ vec a vec b vec c]^=0 d. [ vec a vec b vec c]^=| vec a|^2

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

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 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 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 a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec a .( vec bxx vec c))/( vec b .( vec cxx vec a))+( vec b .( vec cxx vec a))/( vec c .( vec axx vec b))+( vec c . ( vec bxx vec a))/( vec a . ( vec bxx vec c))

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

Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. Let vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c]),a n d vec r=( vec axx vec b)/([ vec a vec b vec c]),dot If x in R^+, then a. x[ vec a vec b vec c]+([ vec p vec q vec r])/x has least value =2 . b. x^4[ vec a vec b vec c]^2+([ vec p vec q vec r])/(x^2) has least value =(3/2)^(2//3) c. [ vec p vec q vec r]>0 d. none of these