Given `vec(A)=4hat(i)+6hat(j)` and `vec(B)=2hat(i)+3hat(j)`. Which of the following

Options

A. `vec(A)xxvec(B)=vec(0)`
B. `vec(A).vec(B)=24`
C. `(|vec(A)|)/(|vec(B)|)=1/2`
D. `vec(A)` and `vec(B)` are antiparallel

Answer

A

Explanation

`vec(A)xxvec(B)=(4hat(i)+6hat(j))xx(2hat(i)+3hat(j))=12(hat(i)xxhat(j))+12(hat(j)xxhat(i))`
`=12(hat(i)xxhat(j))-12(hat(i)xxhat(j))=0`
Again, `vec(A).vec(B)=(4hat(i)+6hat(j)).(2hat(i)+3hat(j))=8+18=26`
Again`(|vec(A)|)/(|vec(B)|)=(sqrt(16+36))/(sqrt(4+9))!=1/2`
Also, `vec(B)=1/2vec(A) rArr vec(A)` and `vec(B)` are parallel and not antiparallel.