Show that the projection vector ` vec aa n d vec b(!= vec0)(com pon e n tof vec aaong vec b)i s(( vec adot vec b)/(| vec b|^2)) vec bdot`

The orthogonal projection of vec a\ on\ vec b is a. (( vec adot vec b) vec a)/(|"a"|^2) b. (( vec adot vec b) vec b)/(| vec b|^2) c. vec a/(| vec a|) d. vec b/(| vec b|)

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=12\ a n d\ | vec a|=2| vec b|

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=13\ a n d\ | vec a|=2| vec b|

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

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 vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

For any tow vectors a\ a n d\ b show that ( vec a+ vec b) ( vec a- vec b)=0 if | vec a|=| vec b|dot

Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot'( vec a- vec b)=8\ a n d\ | vec a|=8| vec b|