What is the area of the rectangle of which `vec(r)=ahat(i)+b hat(j)` is a semidiagonal ?

Given the vectors vec A,vec B, and vec C form a triangle such that vec A=vec B+vec C .find a,b,c, andd such that the area of the triangle is 5sqrt(6) where vec A=ahat i+bhat j+chat kvec B=dhat i+3hat j+4hat kvec C=3hat i+hat j-2hat k

If the area of the triangle the positive vectors of whose vertices are ahat(j), 4hat(j) and hat(i) + hat(j) is 6 square units, find a.

The area of the paralleogram represented by the vectors vec(A)= 2hat(i)+3hat(j) and vec(B)= hat(i)+4hat(j) is

What is the projection of vec(a)=(2hat(i)-hat(j)+hat(k)) on vec(b)=(hat(i)-2hat(j)+hat(k))?

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

Find the angle between the vectors vec(a) and vec(b) , when (i) vec(a)=hat(i)-2hat(j)+3 hat(k) and vec(b)=3hat(i)-2hat(j)+hat(k) (ii) vec(a)=3 hat(i)+hat(j)+2hat(k) and vec(b)=2hat(i)-2hat(j)+4 hat(k) (iii) vec(a)=hat(i)-hat(j) and vec(b)=hat(j)+hat(k) .

If vec(r)=xhat(i)+yhat(j)+zhat(k) , then what is vec(r).(hat(i)+hat(j)+hat(k)) equal to?

If vec a=2 hat i-3 hat j+ hat k ,\ vec b=- hat i+ hat k ,\ vec c=2 hat j- hat k are three vectors find the area of the parallelogram having diagonals ( vec a+ vec b)\ a n d\ ( vec b+ vec c)dot