If ` vec a\ a n d\ vec b` represent two adjacent sides of a parallel then write vectors representing its diagonals.

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)

If vec aa n d vec b are the vectors determined by two adjacent sides of a regular hexagon, what are the vectors determined by the other sides taken in order?

The vectors vec a=3 veci-2 vec j+2 vec k and vec b=- vec i-2 vec k are adjacent side of a parallelogram. Then angle between its diagonals is pi/4 (b) pi/3 (c) (3pi)/4 (d) (2pi)/3

If vec aa n d vec b represent two adjacent sides vec A Ba n d vec B C respectively of a parallelogram A B C D , then show that its diagonals vec A Ca n d vec D B are equal to vec a+ vec b and vec a- vec b respectively.

If vec a ,\ vec b ,\ vec c\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

Write the expression for the area of the parallelogram having vec a\ a n d\ vec b as its diagonals.

If vec a ,\ vec b ,\ vec c are position vectors of the vertices of a triangle, then write the position vector of its centroid.

There are two vector vec(A)=3hat(i)+hat(j) and vec(B)=hat(j)+2hat(k) . For these two vectors- (i) Find the component of vec(A) along vec(B) and perpendicular to vec(B) in vector form. (ii) If vec(A) & vec(B) are the adjacent sides of parallelogram then find the magnitude of its area. (iii) Find a unit vector which is perpendicular to both vec(A) & vec(B) .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .