The vector component of ` vec b` perpendicular to ` vec a` is
a.`( vec bdot vec c) vec a`
b. `( vec axx( vec bxx vec a))/(| vec a|^2)`
c. ` vec axx( vec bxx vec a)`
d. none of these

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 vectors vec aa n d vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to a is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec adot vec b)/(| vec b|^2) c. vec b-( vec bdot vec a)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)

If vectors vec a and vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to veca is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec a. vec b)/(| vec b|^2) c. vec b-(( vec b. vec a)veca)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)

Given the following simultaneous equation for vectors vec xa n d vec y , vec x+ vec y= vec a , vec xxx vec y= vec b , vec xdot vec a=1,t h e n vec x= dot ( vec a+( vec axx vec b))/( vec a^2) (B) ( vec a+( vec axx vec b))/(| vec a|) (C) (( vec a+( vec axx vec b)))/( vec b^2) (D) none of these

Given the following simultaneous equation for vectors vec x and vec y , vec x+ vec y= vec a , vec x xx vec y= vec b , vec x . vec a=1 , then vec x= (A) ( vec a+( vec axx vec b))/( vec a^2) (B) ( vec a+( vec axx vec b))/(| vec a|) (C) (( vec a+( vec axx vec b)))/( vec b^2) (D) none of these

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec vdot vec a=0a n d vec vdot vec b=1a n d[ vec v vec a vec b]=1 is vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^) d. none of these

If vec a is parallel to vec bxx vec c , then ( vec axx vec b)dot( vec axx vec c) is equal to | vec a|^2( vec bdot vec c) b. | vec b|^2( vec adot vec c) c. | vec c|^2( vec adot vec b) d. none of these

If vec adot vec b=betaa n d vec axx vec b= vec c ,t h e n vec b is ((beta vec a- vec axx vec c))/(| vec a|^2) b. ((beta vec a+ vec axx vec c))/(| vec a|^2) c. ((beta vec c- vec axx vec c))/(| vec a|^2) d. ((beta vec a+ vec axx vec c))/(| vec a|^2)

Let vec aa n d vec b be unit vectors that are perpendicular to each other. Then [ vec a+( vec axx vec b) vec b+( vec axx vec b) vec axx vec b] will always be equal to 1 b. 0 c. -1 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